We investigate the CP even and odd Higgs boson production in electron-photon collisions within the framework of standard model (SM) as well as the type-II two Higgs doublet model (2HDM) which includes the minimal supersymmetric standard model (MSSM). We evaluate the scattering amplitude for the $e\gamma$ Higgs boson production at the electroweak one-loop level. The transition form factor of the Higgs boson is introduced. In the case of the SM Higgs boson production, the $W$-boson loop contribution is dominant over that of the
top-quark, while in the case of the CP-odd Higgs boson ($A^0$) the dominant contribution comes from the top-quark loop, because of the absence of the direct coupling of $A^0$ to $W$ and $Z$ boson pairs. We reexamine the possible extra contributions to the $A^0$ production in the MSSM. Some arguments are given toward the analysis of CP-even Higgs production for the MSSM.