In　this　paper,　we　present　a　continued　fraction　product　approximation　for　the　Gamma　function,　via　the　Tri-gamma　function.　This　approximation　is　fast　in　comparison　with　the　recently　discovered　asymptotic　series.　We　also　establish　the　inequalities　related　to　this　approximation.　Finally,　some　numerical　computations　are　provided　for　demonstrating　the　superiority　of　our　approximation.　(c)　2017　Elsevier　Inc.　All　rights　reserved.