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A regular splitting and potential reduction method is presented for solving a quadratic programming problem with box constraints (QPB) in this paper. A general algorithm is designed to solve the QPB problem and generate a sequence of iterative points. We show that the number of iterations to generate an ε-minimum solution or an ε-KKT solution by the algorithm is bounded by O(n^2ε1ε +n(1+2n)), and the total running time is bounded by O(n^2(n+n+1ε)(nε1ε +n)) arithmetic operations. , number=6, journal=Journal of Computational Mathematics, year=2021, month=July, pages=643–652