The trajectory tracking ability of mobile robots suffers from uncertain disturbances. This paper proposes an adaptive control system consisting of a new type of self-organizing neural network controller for mobile robot control. The newly designed neural network contains the key mechanisms of a typical brain emotional learning controller network and a self-organizing radial basis function network. In this system, the input values are delivered to a sensory channel and an emotional channel, and the two channels interact with each other to generate the final outputs of the proposed network. The proposed network possesses the ability of online generation and elimination of fuzzy rules to achieve an optimal neural structure. The parameters of the proposed network are online tunable by the brain emotional learning rules and gradient descent method; in addition, the stability analysis theory is used to guarantee the convergence of the proposed controller. In the experimentation, a simulated mobile robot was applied to verify the feasibility and effectiveness of the proposed control system. The comparative study using the cutting-edge neural network-based control systems confirms that the proposed network is capable of producing better control performances with high computational efficiency.