This study proposes a constraint-following approach for achieving trajectory-tracking control of autonomous underwater vehicles (AUVs). To achieve more precise underwater trajectory-tracking control, the controller design takes into account various underwater disturbances as well as measurement errors during state feedback. Additionally, for the underactuation of AUVs, an uncertainty decomposition method is employed to separate matched and mismatched parts. The controlled system stability is guaranteed based on the Lyapunov stability analysis. Finally, numerical simulations and hardware-in-the-loop simulation results verify the effectiveness and superiority of the proposed trajectory-tracking control method.