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It is believed the device partially exploded as the man drove away from his home in the Sweep Road area of the town. He was not injured in the attack.
The man is a former police officer who currently works as a guard at the town's PSNI station.
PSNI Chief Supt Skuce said those who planted the bomb had "scant regard" for human life.
It is the third attempted car bomb attack on security personnel in the past seven days.
Police said the alert began at about 0800 BST on Tuesday. The Sweep Road has been closed to the Glenavon Hotel as army bomb experts examine the car.
Chief Supt Skuce described the road where the device partially exploded as very busy, especially at that time of the morning.
Last Wednesday, a device fell from the car of an Army major in Bangor and on Saturday, a Catholic police officer was targeted in Kilkeel, County Down.
Dissident republicans have been blamed for the attacks.
'No justification'
Commenting on Tuesday's attack, Sinn Fein MLA Francie Molloy said the man had a "lucky escape" and that the attack was "wrong".
"This man has the right to work anywhere he wishes and should not come under any threat in doing so," he added.
"The groupings behind this, and other attacks earlier in the week, need to come forward and tell the people of Ireland how this will advance the goal of achieving a united Ireland?"
SDLP MLA Patsy McGlone said a number of homes and a nursery in the Glenavon Gardens area had to be evacuated
"Campaigns of violence and intimidation had no justification in the past and have no justification now," he said.