In　this　paper,　we　focus　on　the　two-coupled-oscillator　model　in　optics　chiral　molecular　medium.　We　perform　scale　transformations　for　variables　and　study　the　existence　of　periodic　solutions　in　detail　for　the　two-coupled-oscillator　system.　We　obtain　the　Melnikov　function　by　establishing　the　curvilinear　coordinate　transformation　and　constructing　a　Poincaré　map.　Then　the　existence　of　periodic　solutions　of　this　oscillator　system　is　analyzed　when　unperturbed　system　is　Hamiltonian　system.　We　apply　them　to　discuss　the　upper　bound　of　periodic　solutions　of　this　oscillator　system　and　give　the　configuration　of　the　phase　diagram　by　numerical　simulation.　It　has　great　theoretical　significance　to　study　the　non-planar　motion　of　the　two-coupled-oscillator　system　for　analyzing　dynamic　characteristics　in　optics　chiral　molecular　medium.　©　Published　under　licence　by　IOP　Publishing　Ltd.