In this paper, we consider the control problem of tracking a 3D spatial trajectory for a fully actuated helicopter in static known environment, which is predefined to avoid obstacles and collisions considering the distance, fuel consumption and other related constraints. For this purpose, a nonlinear controller using the radial basis function neural network (RBFNN) is designed. Based on Lyapunov analysis, the proposed adaptive neural network control succeeds in tracking the desired trajectory robustly to a small neighborhood of zero, and guarantees the boundedness of all the closed-loop signals at the same time.Extensive numerical results are given to illustrate the effectiveness of the designed controller.