The man approached the owner of a property on Severn Road in Bloxwich and insisted he needed to carry out work in the garden.
After doing the work, he demanded a large quantity of money and when the homeowner refused, he took his car as payment.
West Midlands Police has now asked people if they recognise him, as they investigate the theft which happened at around 5pm on May 24.
Officers believe two other men were waiting nearby in a white Ford Transit van.
Anyone with information is asked to contact police via live chat on the West Midlands Police website or by calling 101.
Quote crime number 20/448016/22.