Several new precise times of eclipses were measured for eclipsing binary CG Aur as a part of our long-term observational project for studying eclipsing binaries with an eccentric orbit. Based on a current O−Cdiagram, we found for the first time that its orbit is slightly eccentric (e = 0.124) and that times of minima besides the slow apsidal motion show very rapid changes with a period about 700days only, caused very probably by the third body orbiting the eclipsing pair. The relativistic contribution to the total apsidal-motion rate is significant being about 33%.