  Allowing leptoquarks to interact with both right-handed and left-handed
neutrinos (i.e., ``non-chiral'' leptoquarks), we show that a non-zero neutrino
magnetic moment can arise naturally. Although the mass of the non-chiral vector
leptoquark that couples to the first generation fermions is constrained
severely by universality of the $\pi^+$ leptonic decays and is found to be
greater than 50 TeV, the masses of the second and third generation non-chiral
vector leptoquarks may evade such constraint and may in general be in the range
of $1\sim 100$ TeV. With reasonable input mass and coupling values, we find
that the neutrino magnetic moment due to the second generation leptoquarks is
of the order of $10^{-12}\sim 10^{-16} \mu_{\rm B}$ while that caused by the
third generation leptoquarks, being enhanced significantly by the large top
quark mass, is in the range of $10^{-10}\sim 10^{-14} \mu_{\rm B}$.
