This　article　studies　the　Dirichlet　eigenvalue　problem　for　the　Laplacian　equations　Delta　u　=　-lambda　u,　x　is　an　element　of　Omega,　u　=　0,　x　is　an　element　of　partial　derivative　Omega,　where　Omega　subset　of　R-n　is　a　smooth　bounded　convex　domain.　By　using　the　method　of　appropriate　barrier　function　combined　with　the　maximum　principle,　authors　obtain　a　sharp　lower　bound　of　the　difference　of　the　first　two　eigenvalues　for　the　Dirichlet　eigenvalue　problem.　This　study　improves　the　result　of　S.T.　Yau　et　al.