A　cascadic　multigrid　method　is　proposed　for　eigenvalue　problems　based　on　the　multilevel　correction　scheme.　With　this　new　scheme,　an　eigenvalue　problem　on　the　finest　space　can　be　solved　by　linear　smoothing　steps　on　a　series　of　multilevel　finite　element　spaces　and　nonlinear　correcting　steps　on　special　coarsest　spaces.　Once　the　sequence　of　finite　element　spaces　and　the　number　of　smoothing　steps　are　appropriately　chosen,　the　optimal　convergence　rate　with　the　optimal　computational　work　can　be　obtained.　Some　numerical　experiments　are　presented　to　validate　our　theoretical　analysis.