We consider the perturbed mechanics system as the combination of unperturbed system and perturbed terms, we can select a suitable method to obtain the exact conserved quantities I0 of unperturbed system. Based on the characteristic of the approximate conserved quantities, the recursion relations between the first order perturbed coefficient I1 of conserved quantities to the exact conserved quantities I0 and the second order perturbed coefficient I2 to the first order perturbed coefficient I1 of conserved quantities and the exact conserved quantities I0 are established. We calculate the influence of perturbed terms on exact conserved quantities and on the first order perturbed coefficient, according to the recursion relation between the second order perturbed coefficient to the first order perturbed coefficient of conserved quantities and the exact conserved quantities, we obtain the second order approximate conserved quantities of the system by direct integral method. An actual perturbed mechanics system is studied in this paper, and two stable second order approximate conserved quantities are obtained by using this method.