Indefinite quadratically constrained quadratic programs are widely used in fields of chip design, wireless communication network, finance and many practical engineering problems. Up to now, there is still no general global convergence criteria for solving indefinite quadratically constrained quadratic programs, and it brings great challenges. In this paper, the matrix elementary transformation technique is used for transforming the original problem into an equivalent bilinear programming problem. The linear relaxation programming problem is constructed based on the characteristics of the equivalent problem, and by means of the sequential solutions of a series of linear programming problems, the global optimal solution is obtained. The global convergence is proved and some numerical comparison and random experiments are performed, numerical results show that the algorithm is efficient and feasible.