We have studied open charm production in γγ collisions with the TOPAZ detector at the TRISTAN e + e − collider. In this study, charm quarks were identified by electrons (and positrons) from semi-leptonic decays of charmed hadrons. The data corresponded to an integrated luminosity of 95.3 pb −1 at a center-of-mass energy of 58 GeV. The results are presented as the cross sections of inclusive electron production in γγ collisions with an anti-tag condition, as well as the subprocess cross sections, which correspond to resolved-photon processes. The latter were measured by using a sub-sample with remnant jets. A comparison with various theoretical predictions based on direct and resolved-photon processes showed that our data prefer that with relatively large gluon contents in a photon at small x(x ≤ 0.1), with the next-to-leading order correction, and with a charm-quark mass of 1.3 GeV.2