Arthur Harbutt, 78, died after falling outside Go Outdoors at Centaurus Business Park in Cribbs Causeway retail centre in Gloucestershire on March 5, 2018.
Garry Harbutt, 54, was found guilty as sole director of Night and Day Glaziers Ltd at Bristol Crown Court.
Night and Day, based in Titford Road, Oldbury, had been contracted to refit a shop unit at the retail centre.
The incident happened on the morning of March 5, 2018 when the pair were among a group of five men who were moving a large glass panel up some steps on a scaffolding platform.
The scaffolding had no internal edge protection on the side facing into the unit, meaning there was nothing to prevent someone from falling over the unprotected edge.
Arthur, also known as Archie, of Birmingham, had reached the top of the platform when he stumbled and fell from the front of the platform, through the framework of the shop unit and onto a concrete floor.
CPS spokesperson Alyson Harris said: “Garry Harbutt was in charge of operations on the day his father died.
“He failed to ensure that his employees working on the scaffolding had the protection they needed, which led to his father falling and sustaining the injuries that killed him.
“Providing a safe system of work in all areas of construction is essential to prevent such terrible tragedies occurring.”
The prosecution was brought under the Health and Safety at Work Act 1974.
Mr Harbutt will be sentenced on February 7.
Arthur Harbutt was taken to hospital but died from his injuries following the incident, which happened shortly after 8am.
In the aftermath of the tragedy the police and the Health and Safety Executive investigation launched investigations.