This paper proposes a novel tube model predictive control approach for dynamic positioning of autonomous underwater vehicles with state and input constraints. The cost function is selected as a mixture of weighted 1-norms and ∞-norms of states and inputs, which can be reconstructed into linear summation form. Specially, a method is presented to calculate the weighted matrix of the terminal cost so that closed-loop stability is achieved. The proposed control problem can be solved by linear programming, which provides high computational efficiency. Experimental results on “UVIC-I” AUV are conducted to validate the viability and validity of the presented method.