Abstract: Due to there is sharp corners in the continuous straight path and it affects the smoothness of the track in convergence in the Cartesian space. A new speed continuous space linear interpolation algorithm based on the space circular arc transition is put forward on the basis of linear interpolation algorithm and space Spatial arc interpolation algorithm. In other words,eliminating sharp corners by using space arc to transition two adjacent lines. At the same time it proposed a "fitting" concept,to determine the optimal space circular arc by changing the matching degree and determine the corresponding center and radius. The simulation is made through the Matlab at last. The simulation results show that the algorithm is feasibility to meet the requirements of the robot trajectory planning.