In　this　paper,　we　study　locally　projectively　flat　Finsler　metrics　of　constant　flag　curvature.　We　find　equations　that　characterize　these　metrics　by　warped　product.　Using　the　obtained　equations,　we　manufacture　new　locally　projectively　flat　Finsler　warped　product　metrics　of　vanishing　flag　curvature.　These　metrics　contain　the　metric　introduced　by　Berwald　and　the　spherically　symmetric　metric　given　by　Mo-Zhu.