We study a non-minimal holographic superconductors model in both non-backreaction and full-backreaction cases using an analytic approximation, matching method. The matching method is to match the boundary conditions on either the conformal boundary of the AdS spacetime or the event horizon in the bulk spacetime to give an approxiation solution to the fields in the AdS spacetime. In the full-backreaction case, the ordinary matching method with continuous and smooth matching condition is not applicable, so we introduce the generalized matching method that collects all the boundary conditions and relaxes the smooth matching condition for the matching of the gravity field. The condensate of the dilaton and the critical temperature of the phase transition are calculated and we also use the approximated solutions to study the properties of the electric conductivity.