In this paper, we combine the new global optimization method proposed by Qu et al. [S.J. Qu, K.C. Zhang, Y. Ji, A global optimization algorithm using parametric linearization relaxation, Appl. Math. Comput. 186 (2007) 763–771] with a suitable deleting technique to propose a new accelerating global optimization algorithm for solving the non-convex quadratic optimization problems with non-convex quadratic constraints (NQP). This technique offers a possibility to cut away a large part of the currently investigated region in which the global optimal solution of NQP does not exist, and can be seen as an accelerating device for the global optimization algorithm of the NQP problems. Compared with the method in Qu et al. (2007), numerical results show that the computational efficiency is obviously improved by using this new technique in the number of iterations, the required list length and the overall execution time of the algorithm.