It is very important for a robot to obverse its environment in real-time and walk without collision in a crowd. This paper presents a motion planning method, based on visual feedback, for safe Human-Robot Interaction (HRI) in dynamic environments. Firstly, in order to improve accuracy of features marching, Scale Invariant Feature Transform (SIFT) is merged into binocular stereo vision, which is used to detect motion of people. Secondly, by improving Lazy PRM, a robot can find the shortest safe path and move to predetermined destination along the path. Experimental results show that position of people can be detected in real-time in environments with several people walking inside, and the accuracy can reach 96%. Therefore, a robot can arrive at the goal configuration node without collision with people much faster than Lazy PRM.