The noisy environment of the underwater nonlinear under-actuated dynamic system of the Autonomous Underwater Vehicle (AUV) turns out the design of the self-tuning controller, more challenging. In this paper, the Model Reference Adaptive Control (MRAC) along with the Artificial Neural Network (ANN) compensator of the 6 Degree of Freedom (DOF) AUV is illustrated.4 Input-6 Output (4I6O) nonlinear under-actuated dynamic system is divided into first, 4 subsystems and the partial or inverse linearization technique and the coupled linearized model are employed for each one. The stability of the closed- loop subsystems, and hence the complete controlled model is insured according to the Lyapounve's stability theory. To increase the robustness of the closed loop system, an ANN compensator benefiting online backpropagation learning algorithm to tune the network's parameters is incorporated with each controllers. The results of the simulations of the hybrid MRAC along with ANN compensator in Matlab Simulink environment, clearly indicates the outperformance of the ANN compensated control method versus its non-ANN compensated counterpart in terms of increasing the robustness as well as more accurate trajectory tracking performance of the control system subjected to the continual applied noises for both coupled and decoupled dynamical systems.