In　this　paper,　we　extend　the　well-known　Melnikov　method　for　smooth　systems　to　a　class　of　planar　hybrid　piecewise-smooth　systems,　defined　in　three　domains　separated　by　two　switching　manifolds　x　=　a　and　x　=　b.　The　dynamics　in　each　domain　is　governed　by　a　smooth　system.　When　an　orbit　reaches　the　separation　lines,　then　a　reset　map　describing　an　impacting　rule　applies　instantaneously　before　the　orbit　enters　into　another　domain.　We　assume　that　the　unperturbed　system　has　a　continuum　of　periodic　orbits　transversally　crossing　the　separation　lines.　Then,　we　wish　to　study　the　persistence　of　the　periodic　orbits　under　an　autonomous　perturbation　and　the　reset　map.　To　achieve　this　objective,　we　first　choose　four　appropriate　switching　sections　and　build　a　Poincare　map,　after　that,　we　present　a　displacement　function　and　carry　on　the　Taylor　expansion　of　the　displacement　function　to　the　first-order　in　the　perturbation　parameter　epsilon　near　epsilon　=　0.　We　denote　the　first　coefficient　in　the　expansion　as　the　first-order　Melnikov　function　whose　zeros　provide　us　the　persistence　of　periodic　orbits　under　perturbation.　Finally,　we　study　periodic　orbits　of　a　concrete　planar　hybrid　piecewise-smooth　system　by　the　obtained　Melnikov　function.