As the existing dynamic programming algorithm cannot quickly solve Discounted {0-1} Knapsack Problem (D{0-1}KP), based on the idea of dynamic programming and combined with New Greedy Repair Optimization Algorithm (NGROA) and core algorithm, a Greedy Core Acceleration Dynamic Programming (GCADP) algorithm was proposed with the acceleration of the problem solving by reducing the problem scale. Firstly, the incomplete item was obtained based on the greedy solution of the problem by NGROA. Then, the radius and range of fuzzy core interval were found by calculation. Finally, Basic Dynamic Programming (BDP) algorithm was used to solve the items in the fuzzy core interval and the items in the same item set. The experimental results show that GCADP algorithm is suitable for solving D{0-1}KP. Meanwhile, the average solution speed of GCADP improves by 76.24% and 75.07% respectively compared with that of BDP algorithm and FirEGA (First Elitist reservation strategy Genetic Algorithm).