Abstract: For safe path planning of mobile robot in unknown environment, the paper uses a local connected Hopfield neural network (HNN) planner. The stability of the HNN is analyzed, and the condition for the existence of the feasible path(s) is given. If a feasible path(s) exists, the HNN does not have any unexpected local attractive point. The connected weight design considers both "too close" and "too far" to plan the safe path. For the HNN to on-line plan a path on a sequential processor, multi-sequential Gauss-Seidel iteration is used to accelerate the propagation of the HNN potential field. Results demonstrate that the method has good real-time ability and adaptability to environments.