  In this paper, we calculate twist-2 light-cone distribution amplitudes
(LCDAs) of the S-wave and P-wave quarkonia (namely $^1S_0$ state $\eta_{Q}$,
$^3S_1$ state $J/\psi(\Upsilon)$, $^1P_1$ state $h_{Q}$ and $^3P_J$ states
$\chi_{QJ}$ with $J=0,1,2$ and $Q=c,b$) to the next-leading order of the strong
coupling $\alpha_s$ and leading order of the velocity expansion $v$ in the
non-relativistic QCD (NRQCD). We apply these LCDAs to some single quarkonium
exclusive productions at large center-of-mass energy, such as $\gamma^*\to
\eta_Q\gamma, \chi_{QJ}\gamma~(J=0,1,2)$, $Z\to \eta_Q\gamma,
\chi_{QJ}\gamma~(J=0,1,2), J/\psi (\Upsilon)\gamma, h_Q\gamma$ and $h\to J/\psi
\gamma$, by adopting the collinear factorization. The asymptotic behaviors of
those processes obtained in NRQCD factorization are reproduced.
