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This paper presents a new methodology based on neural dynamics for robot path planning by drawing an analogy between cellular neural network (CNN) and path planning of mobile robots. An improved CNN model is established to propagate the target activity within the states pace in the manner of physical heat conduction, which guarantees that the target and the obstacles remain at the peak and the bottom of the activity landscape of the neural network, respectively. The novelty of the proposed neural network model is that local connectivity of neurons is harmonic rather than symmetric in the existing neural network models. The proposed methodology can not only generate real-time, smooth, optimal and collision-free paths without any prior knowledge of the dynamic environment, without explicitly searching over the global free work space or searching collision paths, and without any learning procedures, but it can also easily respond to the real-time changes in dynamic environments. Further, the proposed methodology is parameter-independent and has an appropriate physical meaning.