This　paper　introduce　a　cascadic　multigrid　method　for　solving　semilinear　elliptic　equations　based　on　a　multilevel　correction　method.　Instead　of　the　common　costly　way　of　directly　solving　semilinear　elliptic　equation　on　a　very　fine　space,　the　new　method　contains　some　smoothing　steps　on　a　series　of　multilevel　finite　element　spaces　and　some　solving　steps　to　semilinear　elliptic　equations　on　a　very　coarse　space.　To　prove　the　efficiency　of　the　new　method,　we　derive　two　results,　one　of　the　optimal　convergence　rate　by　choosing　the　appropriate　sequence　of　finite　element　spaces　and　the　number　of　smoothing　steps,　and　the　other　of　the　optimal　computational　work　by　applying　the　parallel　computing　technique.　Moreover,　the　requirement　of　bounded　second　order　derivatives　of　nonlinear　term　in　the　existing　multigrid　methods　is　reduced　to　a　bounded　first　order　derivative　in　the　new　method.　Some　numerical　experiments　are　presented　to　validate　our　theoretical　analysis.