Summary: For a class of non-negative integer quadratic programming problems, a new branch-and-bound reduced method is proposed. In this method, a new rectangular two-partitioned technique and a new linear programming relaxation bounded technique are used. At the same time, in order to improve the degree of approximation and the convergence rate of acceleration, a rectangular reduction strategy is used. Numerical results show that the proposed algorithm is feasible and effective and can solve middle-larger scale problems.