In　this　paper,　we　present　a　new　iterative　algorithm　for　finding　a　common　element　of　the　set　of　fixed　points　of　a　nonexpansive　mapping　and　the　set　of　solutions　of　an　equilibrium　problem,　and　we　prove　the　strong　convergence　theorems　in　Hilbert　spaces.　We　also　apply　our　results　to　the　convex　minimization　and　variational　inequality　problems.　Our　results　extend　and　improve　some　recent　results　of　Cai,　Tang　and　Liu　[Cai,　Y.,　Tang,　Y.　and　Liu,　L.:　Iterative　algorithms　for　minimum-norm　fixed　point　of　nonexpansive　mapping　in　Hilbert　space.　Fixed　Point　Theory　Appl.,　2012:49　(2012)]　and　others.　©　2014,　Forum-Editrice　Universitaria　Udinese　SRL.　All　rights　reserved.