  Extending BLMSSM with exotic Higgs superfields $(\Phi_{NL},\varphi_{NL})$ and
superfields ($Y,Y^\prime$), one obtains the new model called as EBLMSSM, where
exotic leptons are heavy and have tree level couplings with SM lepton. In this
model, some new parameters with CP-violating phases are considered, so there
are new contributions to lepton anomalous magnetic dipole moments (MDMs) and
electric dipole moments (EDMs). Therefore, we study the one-loop, two-loop
Barr-Zee and two-loop Rainbow type corrections to lepton MDMs and EDMs in the
EBLMSSM. Considering the constraints from the lightest CP-even Higgs mass and
decays, we calculate the corresponding numerical results. In our used parameter
space, the new physics contributions to lepton MDMs are large, which can remedy
the deviation between the SM prediction and experimental result well. New
introduced CP-violating phases also affect the lepton EDMs in a certain degree.
