  We consider the two Higgs doublet model (2HDM) along with a generation of
vector-like lepton doublet and singlet to explain the observed discrepancies in
the electron and muon anomalous magnetic moments. The type-X (lepton-specific)
2HDM can allow a light pseudo-scalar which is known to explain the muon
anomalous magnetic moment at two-loop. Such a light particle induces a sizable
negative contribution to the electron anomalous magnetic moment at one-loop in
the presence of vector-like leptons evading all the experimental constraints.
