In order to achieve integration of shaped-profiles parameterization and size optimization of rotor pair for roots pump. From the common circular arc rotor as a example and the conjugate rotation relationship of two identical rotors,full parameter coordinate equation and its corresponding 3 D model are derived in both cases of circular arc as peak profile or circular arc as valley profile. Then,from pitch circle radius and shape coefficient as two design variables,the minimum wrapping cube space volume of rotor pair as an objective function,the upper limit of the shape coefficient and rounded-value of center distance and the diameter ratio of the rotor and other as constraint functions. The size optimization model is derived,then an instance is operated and its results are analyzed. All results show that the two sets of coordinate equations described for rotor shaped-profiles with circular arc as peak profile or circular arc as valley profile is verified absolutely correct by its corresponding3 D parameter model of single part and assembly rotor parts. Only by the three-order polynomial fitting,the fitting accuracy of the volume utilization coefficient is higher to be met the design requirements. The optimization selecting of rotor size is necessity emphasized by the optimal pitch circular radius of 103 mm and the optimal shape coefficient of 1. 394 4,etc. It is concluded that the full parameter optimization design method can be used for other shape rotor of roots pump.