The writers propose a successive improved dynamic programming (SIDP) algorithm for hydropower reservoir operation based on an analysis of concavity, complementarity, and monotonicity of hydropower problems. For single-period hydropower generation, storage and release have diminishing marginal contributions to hydropower generation (i.e.,concavity), and there is also a complementary effect between storage and release (i.e.,release becomes more productive in accordance with increasing storage). For multiple-period hydropower generation, the complementarity influences the concavity of the objective function and the monotonicity of operation decisions, and is the major cause of complexity in hydropower operation. With mathematical derivations, the writers propose a concave approximation to the hydropower generation function and a SIDP algorithm for hydropower reservoir operation. The efficiency of SIDP is demonstrated with two hypothetical case studies of long-term hydropower scheduling, which shows that the computation time of SIDP increases linearly in accordance with the number of storage intervals [i.e.,O(n)], whereas dynamic programming (DP) shows a quadratic increase [i.e.,O(n2)].