Abstract: A novel parabolic rotor of Roots pump was developed.The mathematical study of parabolic rotor included:the formulation of geometric relationship,parameterization of 3 D model,derivation of ideal and realistic shape-profiles,upper-limits of shape-factor and coordinate equation.The upper-limits of shape-factor for 2-,3-and 4-lobes were 1.4871,1.3865 and 1.3159,respectively.The influence of the pitch-circle radius and shape-factor on Roots pump's volume,approximated by a wrapping cubic volume of rotor-pair,was investigated for design optimization.The optimized parabolic rotor with 3-lobes was simulated.The results show that the new parabolic rotor is capable of reducing the conjugate leakage and easing the dynamic imbalance because of larger integrated curvature radius and simpler geometric feature at the top.However,its optimal shape-factor was 1.367,instead of 1.3865,suggesting a further design optimization of rotor geometry.