A novel biologically inspired neural network approach is proposed for real-time simultaneous map building and path planning with limited sensor information in a non-stationary environment. The dynamics of each neuron is characterized by a shunting equation with both excitatory and inhibitory connections. There are only local connections in the proposed neural network. The map of the environment is built during the real-time robot navigation with its sensor information that is limited to a short range. The real-time robot path is generated through the dynamic activity landscape of the neural network. The effectiveness and the efficiency are demonstrated by simulation studies.