The Higgs boson production through electromagnetic process in the exclusive p–p and Pb–Pb ultra-peripheral collisions is calculated. According to the condition of conference, the equivalent photon approximation formulation is used, and the limitations of the variables in the calculations are obtained. Three kinds of the equivalent photon spectrums are considered: the plane wave form, the approximate plane wave forms of Dress et al., and the semi-classical form. For comparison, the gluon–gluon fusion and intrinsic heavy flavors contributions are presented. The numerical results show that, the plane wave photon spectrum with correct limitations of the variables provides more reasonable results for the exclusive p+p→p+p+H and Pb+Pb→Pb+Pb+H processes, and the electromagnetic process provides meaningful contributions for the exclusive Higgs production in ultra-peripheral collisions.