Perturbation method and Poincaré mapping method were used to derive the generalized Melnikov function of the periodic solution for a two-degree-of-freedom vibro-impact system with cubic non-linearity and external excitations. By using the Melnikov′s method, the characteristics of periodic motions with double-impact of the 2-dof system were studied, and the existence condition of period-2 motions with double-impact was determined as a critical curve in the parameter domain. The results of numerical simulations show that the regions below the critical curve are the period-2 motions with double-impact, the upper regions of the critical curve are not period-2 motions with double-impact；Meanwhile，increasing the force amplitude and keeping the other parameters unchanged, the motion state of the system changes from multi-period motions with multi-impact to period-2 motions with double-impact, while increasing the system restitution coefficient and keeping the other parameters unchanged, the motion state of the system changes from period-2 motions with double-impact to multi-period motions with multi-impact.