The cross section for muon pair productions by electrons scattering over ph
otons, sigma (MPP), is calculated analytically in the leading order. It is
pointed out that for the center-of-mass energy range s greater than or equa
l to 5m(mu)(2), the cross section sigma (MPP) is less than 1 mub. The diffe
rential energy spectrum for either of the resulting muons is given for the
purpose of high-energy neutrino astronomy. An implication of our result for
a recent suggestion concerning the high-energy cosmic neutrino generation
through this muon pair is discussed.