This paper proposed a new and effective parametric curve interpolation algorithm with error compensation capability for high speed machining. The proposed algorithm is developed from the first-order Taylor expansion interpolation algorithm and the speed-controlled interpolation algorithm. It is also incorporated the geometry features of the machined curves, the dynamic characteristics of machine tools and the adaptive error control. The proposed algorithm achieves high surface accuracy and avoids feedrate fluctuations. Simulation results have demonstrated the effectiveness and satisfactory performance of the proposed algorithm.