This article presents a design method for the three-dimensional trajectory tracking control of an underactuated autonomous underwater vehicle with unknown current disturbances. To simplify the complexity of the controller and avoid the singular problem induced by initial state constraints, a novel nonlinear backstepping technique based on virtual control variables is employed to design the kinematics and dynamics controllers. The control law is developed by building virtual errors, which can solve the problem of differential explosion in the traditional backstepping. Specifically, an ocean current observer based on the kinematics model is proposed to estimate unknown current disturbances, where the estimation is integrated into the autonomous underwater vehicle kinematics and dynamics equations. The convergence of tracking errors and system stability are proven by using Lyapunov stable theory. Finally, the simulation studies were provided to illustrate the effectiveness and good performance of the above trajectory tracking strategy.