In this paper, a novel neurobiologically-inspired intelligent tracking controller is developed and implemented for unmanned aircraft systems in the presence of uncertain system dynamics and disturbance. The methodology adopted, known as Brain Emotional Learning Based Intelligent Controller (BELBIC), is based on a novel computational model of emotional learning within brain limbic systems in mammals. Compared to conventional model-based control methods, BELBICs are more suitable for practical unmanned aircraft systems since they can maintain the real-time unmanned aircraft system performance without known system dynamics and disturbance. Furthermore, the learning capability and low computational complexity of BELBIC mean that it is very promising for implementation in complex real-time applications. Moreover, we proved that our proposed methodology guarantees convergence. To evaluate the practical performance of our proposed design, BELBIC has been implemented into a benchmark unmanned aircraft system. Numerical and experimental results demonstrated the applicability and satisfactory performance of the proposed BELBIC-inspired design.