A biologically inspired neural computation model is proposed for dynamic planning and tracking control of robots. The dynamic environment is represented by a neural activity landscape of a topologically organized neural network, where each neuron is characterized by a shunting equation. The collision-free path is generated in real-time through the activity landscape without any prior knowledge of the dynamic environment. The real-time tracking control of robots to follow the planned path is also designed using shunting equations. The effectiveness is demonstrated through case studies. Simulation in several computer-synthesized virtual environments further demonstrates the advantages of the proposed approach.