  The process of exclusive electroproduction of vector quarkonium (EEQ), $e
p\to epV$, is per se an interesting topic in studies of quarkonium production
mechanism, QCD description of diffractive interaction and nucleon structure. We
investigate this process in the framework of nonrelativistic QCD and QCD
collinear factorization at the next-to-leading order QCD accuracy. The
perturbative convergence behavior is discussed in a large range of photon
virtuality $Q^2$. The $J/\psi$ large-$Q^2$ electroproduction data at HERA can
be well explained, and the $\Upsilon$ differential production rate is
predicted. The uncertainties in theoretical predictions with radiative
corrections are greatly reduced. Notice the EEQ process is extremely sensitive
to the gluon distribution in nucleon, the generalized parton distribution, our
results will constraint the gluon density with high precision while confronting
to the future experimental data. For the sake of comparing convenience, the
analytic expressions are provided.
