  We employ the Boltzmann transport model to study the charmonium regeneration
with non-thermal charm quarks in relativistic heavy-ion collisions. As heavy
quarks do not reach kinetic thermalization in the quark-gluon plasma (QGP), the
final transverse momentum distribution of regenerated charmonium depends on the
degree of charm quark kinetic thermalization. When the charm momentum
distribution becomes harder, more charm quarks are distributed in the middle
and high $p_T$, where the production of regenerated charmonium also becomes
larger. With non-thermal momentum distribution of charm quarks in their
coalescence process, the nuclear modification factor $R_{AA}(p_T)$ of
charmonium enhances at middle $p_T$. Besides, the elliptic flow $v_2(p_T)$ of
charmonium also enhances at middle $p_T$ as more regenerated charmonium are
distributed in this $p_T$ region. The theoretical calculations with non-thermal
charm distribution explain well the $p_T$ dependence of charmonium $R_{AA}$ and
$v_2$, which indicates that charm quarks do not reach complete kinetic
thermalization in the QGP when charmonium are regenerated.
