The existence of infinite solutions of KleinGordonMaxwell system with coercive potential is studied and proved under local (AR) condition. The unique term φ of the system is implicit function, which can’t be expressed by u. Some techniques of lemmas and analysis are used to overcome this difficulty. Based on variational principle, the existence of infinite solutions of KleinGordonMaxwell system with coercive potential is proved. The system with compulsory potential has the geometric structure of mountain path and satisfies (PS) condition. Combining with the symmetric mountain path lemma, the results of the existence of infinite solutions of the system are obtained.