In the trajectory planning of industry robot in Cartesian space,a small “arc-curve” is always used to connect two trajectories in order to change the moving direction smoothly without decreasing velocity down to zero.It requires trajectory smooth enough to turn the direction during a high-speed and high-precision operation of industry robot.However,the small “arc-curve” would bring mutations to the trajectory of acceleration.To avoid such disadvantage,a new connection method based on 5th-order polynomial interpolation was proposed,and some derivations which showed how to compute the coefficient matrix of the polynomial were listed.The simulation attests that the new method connects two trajectories more smoothly.