Acceleration response characteristics of a five-support counter-rotating dual-rotor system are studied. The transient dynamic model of the experimental counter-rotating dual-rotor system is established with finite element analysis software and fixed interface modal synthesis method. The acceleration time-domain characteristics, precession speed variation characteristics and the change laws of centroid of every disk in the rotor system are analyzed in the acceleration process. The study results show that: acceleration response characteristics of various cross-sections have a close relation with critical speeds and mode shapes of the rotor system; complex nonsynchronous precession exists in the acceleration process; centroid shift of inner and outer rotor occurs to their incentive critical speed respectively. Experimental verification was carried out, calculation results are in good agreement with experiment data.