This paper presents the novel Hybrid DirectIndirect Adaptive Generalized Dynamic Inversion (HDI-AGDI) based attitude control of Autonomous Underwater Vehicle (AUV). The two-loops structured control system is proposed having outer (slow) positional loop and inner (fast) attitude loop. The outer loop incorporates Proportional- Derivative control, which generates the desired pitch and yaw attitude commands based on the positional errors, to the inner attitude loop. The inner loop in turns engaged the HDI-AGDI control approach to track the desired pitch and yaw attitude profiles by providing the required control deflections. The proposed HDIAGDI approach comprised of direct and indirect forms of adaptive control. In direct AGDI control, dynamic constraint is prescribed based on the attitude deviation function and its inverse is computed by using Moore-Penrose Generalized Inverse (MPGI) to realize the control law. The null control vector uses Lyapunov based proportional gain matrix to guarantee asymptotic stability to angular body rate dynamics. To provide robustness, an additional term based on sliding mode control with adaptive modulation gain, is integrated with the control structure. On the other hand, the indirect AGDI control utilizes neural networks for online estimation of the unknown parameters of the nonlinear attitude dynamics, whose weight vectors are updated online using Lyapunov principle. The singularity problem is addressed by including a dynamic scaling factor in the expression of MPGI. The semi-global practically stable attitude tracking is guaranteed by using positive definite control Lyapunov function. For performance evaluation, numerical simulations are conducted on the six degrees of freedom simulator of the Monterey Bay Aquarium Research Institute AUV under nominal and perturbed marine conditions.