In this work, we present a new radius for a modified trust region method and used them to solve the large-scale unconstrained optimization. Our approach increases and improves the robustness and efficiency of the trust-region frameworks as well as decrease the computational cost of the algorithm by decreasing the number of the trust-region subproblems that must resolved when the trail step rejected. Theoretical analysis shows that the new approach conserve the global convergence to the first-order critical points under classical assumptions.