To grasp a feasibility of back fire control by valve overlap period, back fire limit equivalence ratio was estimated with valve overlap period which has the same supply energy and positive intake pressure as valve overlap period $300^{circ};CA$. As the result, it was shown that the smaller valve overlap period has the higher back fire limit equivalence ratio under valve overlap period $300^{circ};CA$ as well as VOP $0^{circ};CA$. This result means that expansion of back fire equivalence ratio by decreasing valve overlap period was caused by decrease of back flow duration of flame from in-cylinder to intake port than decrease of lower supply energy.