The existing trapezoidal acceleration and deceleration calculation method has been widely used in machine tools， hydraulic and other heavy equipment， but its initial and final speed is zero， which does not meet the needs of service robots. In this paper， a method of acceleration and deceleration of flexible class trapezoid with non-zero initial velocity is proposed by means of mathematical derivation and experiment. Four kinds of motion strategies are planned according to different running distances， and the conditions of switching non-tolerance strategies are analyzed. In order to verify the feasibility of the algorithm， the test was carried out on the servo test bench. The results show that motion planning can be interrupted by the trapezoidal acceleration and deceleration method， and motion planning can be redone when the initial velocity is not zero. The algorithm in this paper can meet the requirements of flexible acceleration and deceleration of robots under different motion states.