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This paper proposes a robust H2 optimal control strategy for the depth-plane motion of an autonomous underwater vehicle (AUV) in the presence of output disturbances and time delay. The six degrees of freedom nonlinear kinematic and dynamic equations of motion of the vehicle are firstly described. The depth-plane linearization of the vehicle equations of motion is then derived for efficient controller design from the practical point of view. Using this linearized and reduced-order model, a robust H2 optimal control method is designed. The designed control method takes into account both the output disturbances and time delay and provides suitable control action for desired tracking. The robust stability and robust performance of the proposed control method with respect to the model uncertainties are discussed. Simulation studies demonstrate that the proposed robust H2 optimal control strategy has remarkable performance and provides higher tracking accuracy, better output disturbances rejection ability, stronger robustness against model uncertainties, and smaller fin angle input than the existing pitch-and-depth loop PD depth controller.