Zimmer, a native of Angola, Indiana, began studying the violin at age four. He became the youngest member of the Fort Wayne Philharmonic at 16. Shortly after graduating high school, he joined the first violin section of the Indianapolis Symphony.
After fourteen years with the ISO, he joined the Cleveland Orchestra in 1966 and played with the ensemble for 36 years.
Zimmer also had stints teaching at Butler and DePauw Universities and played in chamber groups including the Indianapolis Baroque Ensemble.
He performed often with his wife Betty, a pianist.