This　paper　introduces　a　kind　of　multigrid　finite　element　method　for　the　coupled　semilinear　elliptic　equations.　Instead　of　the　common　way　of　directly　solving　the　coupled　semilinear　elliptic　problems　on　some　fine　spaces,　the　presented　method　transforms　the　solution　of　the　coupled　semilinear　elliptic　problem　into　a　series　of　solutions　of　the　corresponding　decoupled　linear　boundary　value　problems　on　the　sequence　of　multilevel　finite　element　spaces　and　some　coupled　semilinear　elliptic　problems　on　a　very　low　dimensional　space.　The　decoupled　linearized　boundary　value　problems　can　be　solved　by　some　multigrid　iterations　efficiently.　The　optimal　error　estimate　and　optimal　computational　work　are　proved　theoretically　and　demonstrated　numerically.　Moreover,　the　requirement　of　bounded　second-order　derivatives　of　the　nonlinear　term　in　the　existing　multigrid　method　is　reduced　to　a　Lipschitz　continuous　condition　in　the　proposed　method.