Assuming that neutrinos have non-vanishing magnetic moments, we discuss the possibility of pair production through annihilation of charged fermions in high-energy collisions. Adopting the Pauli interaction for photon-neutrino coupling, we calculate t
he neutrino pair production cross section in the photon channel and compare the result with the standard model in $ Z^{0} $ channel. we demonstrated that the enhancement of the production rate for Majorana neutrino pairs over the standard model rate can be possible at the center-of-mass energy of $10 - 100$ TeV for the Large Hadron Collider or the ultra-high-energy cosmic Ray when the transition magnetic moment is not smaller than $10^{-9} - 10^{-10} mu_B$.
