Nikki Sinclaire, who represented the West Midlands region in Brussels and Strasbourg until 2014, signed and submitted "significant" expenses "in excess of the flight costs", according to the prosecution.
The jury was told that in one case Sinclaire would have needed a car that could "travel back in time", based on the receipts she is accused of submitting.
Antonie Muller, prosecuting, said Sinclaire submitted 10 false claims through "dishonesty and deception" rather than in error.
Mr Muller said that in another claim, from October 10 2009, Sinclaire claimed she had driven from Solihull to Stoke-on-Trent when she was in Cyprus.
The prosecution produced a Hilton hotel receipt from Nicosia alleged to show Sinclaire buying a Kit-Kat, a drink, and later "some hairdressing" the same day.
Mr Muller said: "She claimed she travelled 127 miles (to Stoke) when you know she hadn't even been in the country."
Documents seized by police allegedly show Sinclaire received a Greek parking ticket for 25 euros while on the island.
He added that investigation of the UK's automatic number plate recognition cameras found Sinclaire never made the trip to Staffordshire, as she claimed.
Opening the prosecution's case in what is scheduled to be a three-week trial at Birmingham Crown Court, Mr Muller said: "In short, this is a case about a member of the European Parliament, an elected official, making false and dishonest claims for travel expenses during her office.
"Specifically, during the period in the latter part of 2009 to the summer of 2010.
"The Crown rely on a series of claims for travel expenses made by Miss Sinclaire.
"We contend - and I believe it is not really disputed - these claims are probably false and do not reflect the travel expenses that were actually incurred.
"Neither do they they represent the forms of travel actually taken.
"We allege Miss Sinclaire made false claims broadly of two different varieties.
"On some occasions she would claim for travel which she had not undertaken at all.
"On other occasions she made false claims for travel which enabled her to claim significantly higher sums than if she had correctly stated travel she'd actually undertaken."
He told the jurors it may "seem odd" that travelling by car could be more financially advantageous than going by plane, but not when including the Brussels parliament's "travel time" allowances.
The Crown's barrister said six of the 10 claims saw Sinclaire claim for car and ferry travel when she had flown via Paris Charles de Gaulle Airport, Basel in Switzerland or Brussels.
Mr Muller said EU expenses files showed she had submitted Brussels Airlines boarding passes - with a request for "extra leg room" - for a return flight on October 9 2009, when she was in Cyprus.
On another occasion, she claimed a 1,271-mile round trip from her Solihull home to Strasbourg, by car, he said, but she allegedly flew from London Heathrow to Basel, returning on January 21 2010, where she booked herself into a Hilton Metropole hotel in London.
He said: "The air fares cost £130. The 1,200-odd miles of vehicle travel was worth in excess of 900 euros (£750)."
The Crown said Sinclaire submitted that claim - with a ferry booking made three hours before travel - supported by French toll road tickets and a petrol station receipt from 11.32am on January 18 2010.
Mr Muller said: "The ferry was only supposed to arrive at Dunkirk at 1pm, so unless that car can travel back in time, it is impossible for that to have happened."
He added that similar allegedly false expense claims were submitted for October 19-23 2009, and then November 23-26.
Mr Muller said Sinclaire then put in a claim "just shy of 400 euros" for a 484-mile round trip from Solihull to Chester-le-Street on January 8 2010.
The court heard the MEP's colleague had travelled to County Durham by train to collect a £6,000 Mercedes Vito for Sinclaire, while she was having lunch with an NFU official in Stratford-upon-Avon.
The 47-year-old, of Shirley, Solihull, West Midlands, is accused of misconduct in a public office between October 1 2009 and July 31 2010 while a serving member of the European Parliament by making or causing to be made false or dishonest claims for travel expenses.
She is further charged of fraudulently transferring criminal property into her bank account between October 14 2009 and December 31 2010.
At the start of the trial, Judge Stephen Eyre QC told the jury: "This is not a trial about politics, but about particular events in a particular time and about the intention of which certain things were done.
"Whether you agree or disagree with the defendant's politics is irrelevant to this trial."
Sinclaire, on bail, denies all the charges and the trial continues.