The first-order revision and the approximation analytical formula of the energy levels for hydrogen-likeatoms under the condition of Debye shielding potential are achieved by means of the Rayleigh-Schrodinger perturbationtheory; meanwhile, the corresponding recurrence relations are obtained from the use of the solution of power series. Basedon the above solutions and with the use of energy consistent method the equivalent value of second-order reversion underthe condition of Debye shielding potential is produced as well and the result is compared with the data obtained by thenumerical method. Besides, the critical bond-state and corresponding cut-off conditions are discussed.