Andrew McNicoll, 43, from Balerno, was taken to hospital after the crash on Lanark Road in January. He later died.
Police said he had been cycling on the north carriageway of the road at the time of the crash and hit a parked car.
The concert at Polwarth Parish Church is being held at 19:30 on Friday to raise money for his parent's campaign for safer roads.
Following the crash a man was detained by police in connection with the incident but later released without charge. Police said inquiries are ongoing.
At the time Mr McNicoll's father Ian said: "Our grief, as you can imagine, is immense.
"Andrew was a fit young man with a great future ahead of him with his partner Donna.
"We are extremely proud of our Andrew and his achievements, and are devastated to have lost him."
He added: "We are setting up a memorial fund in his name to help make cycling safer in Scotland."
A benefit concert in memory of a cyclist killed on an Edinburgh road is to be held in an Edinburgh church.