To capture the accurate hysteretic characteristics of a rotary magnetorheological (MR) damper in reciprocating motion, a new model with reversibility is proposed and analyzed. The rotary MR damper in helical flow mode is designed and tested on MTS under different current to obtain the hysteretic characteristics. To portray hysteresis effectively and accurately, the proposed model composed of a shape function and hysteresis factor is introduced. To obtain the reversibility, the model is separated to the hysteretic part and current-dependent part based on normalization method. The two parts follow the multiplication rule. To improve computational efficiency, Constriction Factor Particle Swarm Optimization (CFPSO) algorithm is used to identify the model’s parameters. Feasibility and effectiveness of the identified model are validated through comparison with two typical dynamic models.