Using Muller matrix and Stokes parameter,transmission and half breadth of passband of tunable Lyot filter were theoretically analysed,and the effect that the accuracy of quarter wave plate made to the character of filter was first discussed.The results show that Lyot birefrigent tunable filter has such properties as favorable tunability,wide tunable range and so on.The accuracy of quarter wave plate will do not any impact on half breadth of passband of filter,but may cause the moving of transmission spectrum.