In this paper, we show the geometry meaning of the maxima of theCDT subproblem’s dual function. We also studied the continuity of the global solution of the trust region subproblem. Based on an approximation model, we prove that the global solution of the CDT subproblem is given with the Hessian of Lagrangian positive semi-definite by some specially-located dual maxima and by restricting the location region of the multipliers which corresponding a global solution in other cases.