Fixed　point　computation　plays　an　important　role　in　the　field　of　engineering　calculation.　Rounding　errors　often　cause　no　convergence　for　iteration　sequence　or　results　distortion　in　many　fixed　point　iterative　method.　In　this　paper,　we　prove　the　strong　convergence　of　an　iterative　method　for　finding　a　common　element　of　the　set　of　solutions　of　mixed　equilibrium　problems　and　the　set　of　fixed　points　of　a　finite　family　of　nonexpansive　mappings　under　some　suitable　conditions.　Result　presented　in　this　paper　improves　and　extends　the　recent　known　results　in　this　area.