A direct treatment of the min-max type objective function of the dynamic response optimization problem is proposed. Previously, the min-max type objective function was transformed to an artificial design variable and an additional point-wise state variable constraint function was imposed, which increased the complexity of the optimization problem. Especially, the design sensitivity analysis for the augmented Lagrangian functional with the suggested treatment is established by using the adjoint variable method and a computer program to implement the proposed algorithm is developed. The optimization result of the proposed treatment are obtained for three typical problems and compared with those of the previous treatment. It is concluded that the suggested treatment in much more efficient in the computational effort than the previous treatment with giving the similar optimal solutions.