In the X-C linkage grinding of non-circular parts, the computation and control method of contour error in polar coordinates platform is different with that in the XY coordinates platform. To solve this problem, the analysis of the definition and computation methods for contour error and track error in polar coordinates platform will be made. Through the relative lead-lag relation of the linkage axes in the grinding process, the range of the estimation contour error is narrowed and a contour error calculation model is constructed. Then the contour compensation controllers along contour error direction and trajectory tracking error direction are designed respectively, and the error compensation decoupling matrix of the X-C linkage axes is given as well. In the end of this paper, we take the machining of the cylinder contour in Wankel rotary piston engine as an example. A simulation experiment of contour error compensation control based on relative lead-lag quantity is made. The result shows that the designed contour compensation controller can increase the contour machining accuracy effectively.