We employ the improved variational-perturbation method based on integral equation (variational-integral perturbation method) to solve the heavy quarkonium in the 2S state. Setting the mother Hamiltonian including variational parameter as the zero-order Hamiltonian and choosing the exact solution of the mother Hamiltonian system as the trial wave function, we obtain the multi-order corrected wave functions consisting of a few terms and calculate the multi-order energy corrections. The corrected wave functions are quadratically integrable and the energy corrections are in good agreement with the exact data. The boundedness and convergence of the perturbation series solution are also verified. The results show that the variational-integral perturbation method can not only raise precision of the result but also keep convergence of the wave function.