In　this　paper,　the　authors　primarily　explore　a　delayed　competitor-competitor-mutualist　Lotka-Volterra　model,　which　is　a　system　of　differential　equation　with　infinite　integral.　The　authors　first　study　the　existence　of　positive　periodic　solutions　of　the　model　by　using　the　Krasnoselskii＇s　fixed　point　theorem,　and　then　present　an　example　to　illustrate　the　main　results.