A novel birefringent depolarizer whose optical axes are fan-shaped distribution is designed. Using the idea of superposition of transmitted light, the depolarization performance for linearly polarized light is studied. And the formula of degree of depolarization (D) is obtained. The theory shows that D changes periodically with the vibration azimuth angle (VAA) of incident light and optical path difference (OPD) on the basis of large enough wedge angle. D is 100% when VAA takes (N/2)π (N is integer), independent of the OPD. And D is the worst when VAA takes (2N+1)π/4. Adjusting the incident angle is adopted to improve D. The experiment results accord with the theory. And the D value of sample is over 98.84% for any VAA when the incident angle is 4°. So the design is feasible and the research method is so simple and clear that it can provide a new reference for the study of depolarizer.