In view of the problem of inflow delay in medium-term operation of cascade hydropower stations, a concept of delayed energy is introduced, and a stored energy maximization model was constructed for the end of the operation period. A Lagrange relaxation method based on a two-stage subgradient algorithm used to update multipliers is proposed to solve the model. In the first stage, the initial multipliers are rapidly determined by increasing coefficients gradually. In the second stage, the convergence speed is increased by decreasing coefficients gradually. The proposed model and solution method were applied to medium-term optimal operation of six hydropower stations located in the middle and lower reaches of the Lancang River. The results show that the proposed method can obtain good solutions, considering delayed energy can increase stored energy of the hydropower system for the end of the operation period, and the post-effect of medium-term operation should be considered sufficiently.