Using the effective Lagrangian method, we analyze the electroweak corrections to the anomalous dipole moments of lepton from some special two-loop topological diagrams which are composed of neutralino (chargino) - slepton (sneutrino) in the minimal supersymmetric extension of the standard model (MSSM). Considering the translational invariance of the inner loop momenta and the electromagnetic gauge invariance, we get all dimension 6 operators and derive their coefficients. After applying equations of motion to the external leptons, the anomalous dipole moments of lepton are obtained. The numerical results imply that there is a parameter space where the two-loop supersymmetric corrections to the muon anomalous dipole moments may be significant.

Revtex, 45 pages, including 8 figs