The dimension accuracy of the part is directly affected by the contour error. The improvement of contour accuracy has been one of the research hotspots in five-axis Computer Numerical Control (CNC) machining. Because of the inexplicit mathematical expressions of the point-to-curve distance function for free-form parameterized splines, most existing contour error estimation algorithms of the multi-axis CNC machining are based on linear or circular approximation, while the geometric characteristics of the tool path are not taken into account. However, the corner smoothed five-axis tool paths are composed of straight lines and micro splines with few control points, which have clear and simple mathematical expressions and make it possible to directly calculate the contour error from the actual tool pose to the reference tool path. Considering the geometric characteristics of the corner smoothed five-axis tool paths, this paper proposes an on-line and high-accuracy contour error estimation algorithm for five-axis CNC machining. The estimated contour error components of each axis are compensated to the position-loop controller of each axis to realize contour error control. Simulation and experimental results show that the proposed method has higher precision than the state of art methods, and contour errors are effectively suppressed by on-line compensation.