Variable reluctance (VR) resolvers are universally employed as the absolute position sensor in motor control systems. In this paper, a 4-pole 16-tooth VR resolver is proposed with the novel sinusoidal-reluctance rotor contour, and its operation feasibility is evaluated via the analytical investigation and finite element (FE) analysis. Considering the slot and air-gap flux leakage, the original third-order harmonic from the sinusoidal-reluctance rotor contour can be compensated to suppress the total harmonic distortion (THD) in the envelope. And the magnitude of the compensation third-order harmonic can be regulated by adjusting the tooth width. Under 4 mm tooth width, the THD of the cosine envelope with the proposed rotor contour can be limited to only 0.54%, and the angle error can also be restricted to only 0.012 degree (0.72 arc min).