The nonlinear Schrdinger equations are widely used in the fields of quantum mechanics, nonlinear optics, etc. in mathematical physics problems, the nonlinear Schrdinger coupled systems have become a research hotspot. The conditions for the optimization and improvement of the nonlinear terms and the periodic function problems are among more difficult parts, a class of nonlinear Schrdinger coupled system equations with multiple periodic functions is proposed for the coupling problem of this definition on unbounded regions.Based on variational method and some analytical techniques, the solutions of this kind of systems are transformed into the critical points problem of the corresponding energy functional; when the system satisfies the appropriate conditions, it can be verified that the energy functional satisfies the mountain geometry, and a set of bounded nonnegative (Ce)c sequences is obtained and reused. The compactness principle is used in two cases to obtain the existence of nontrivial nonnegative solutions.Finally, the existence of positive solutions of such systems is obtained by the strong maximum principle,it promotes the existing research results.