Because the problem of quadratic program has received extensive attention and research in the field of continuous and combinatorial optimization since the semidefinite planning (SDP) relaxation method was proposed, because the effectiveness of the solution of SDP by using CVX software relies on the primal SDP and dual SDP, this paper proposes to use the strong duality theorem and Gershgorin circle theorem to prove the existence of the solution of SDP relaxation model of convex quadratic program under the condition of box constraints and unit spherical constraints. The new proof method of the existence of the solution of the SDP lays the theoretical foundation of the effectiveness for solving the SDP relaxation model by the CVX software with the two kinds of interior point algorithms of SeDuMi and SDPT3. Once this method is used to prove the existence of the solution of SDP, it is necessary to use CVX software to receive effective solution.