Abstract: In this study, a deterministic global optimization algorithm is proposed for globally solving the Nonconvex Quadratic Programming (NQP). In this algorithm, by using the characteristic of the NQP, a new linearization approach is presented. By utilizing the approach, the linear programming relaxation problem of the NQP is established. The proposed deterministic algorithm is convergent to the global optimum of the NQP by solving a series of linear programming relaxation problems. Compared with the known approaches, numerical results demonstrate the effectiveness of the proposed algorithm.