In this paper an approach-angle-based three-dimensional path-following control scheme has been proposed for underactuated Autonomous Underwater Vehicle (AUV) which experiences unknown actuator saturation and environmental disturbance. First, the path-following error dynamic model is derived based on the principle of relative motion which was followed by the design of approach-angle-based guidance law in both horizontal and vertical profiles of AUV to transform the three-dimensional tracking errors into heading angle and elevation angle tracking errors. The kinematic control law is designed based on the Lyapunov theory and backstepping technique. Second, the kinetic controller is designed based on the Lyapunov theory, backstepping technique and fuzzy logic system approximation method. The indirect adaptive fuzzy logic system is applied to approximate unknown smooth functions which are composed of coupled AUV hydrodynamics and complex differentials of desired pitch and yaw velocities. Moreover, the application of fuzzy control completely free from dependence on accurate AUV kinetic model. Considering a disturbance-like term, which is comprised of fuzzy logic system approximation error and bounded ocean disturbance, an adaptive law is designed to estimate the bound of it. Finally, two sets of comparative numerical simulations, including straight path following with different initial posture and spatial helix path following with sudden disturbance, are studied to illustrate the effectiveness and robustness of the proposed control scheme.