  Some repeating fast radio burst (FRB) sources show high burst rates, and the
physical origin is still unknown. Outstandingly, the first repeater FRB 121102
appears extremely high burst rate with the maximum value reaching
$122\,\mathrm{h^{-1}}$ or even higher. In this work, we propose that the high
burst rate of an FRB repeater may be due to plate collisions in the crust of
young neutron stars (NSs). In the crust of an NS, vortex lines are pinned to
the lattice nuclei. When the relative angular velocity between the superfluid
neutrons and the NS lattices is nonzero, a pinned force will act on the vortex
lines, which will cause the lattice displacement and the strain on the NS crust
growing. With the spin evolution, the crustal strain reaches a critical value,
then the crust may crack into plates, and each of plates will collide with its
adjacent ones. The Aflv\'en wave could be launched by the plate collisions and
further produce FRBs. In this scenario, the predicted burst rate can reach
$\sim 770\,\mathrm{h}^{-1}$ for an NS with the magnetic field of
$10^{13}\,\rm{G}$ and the spin period of $0.01\,\rm{s}$. We further apply this
model to FRB 121102, and predict the waiting time and energy distribution to be
$P(t_{\mathrm{w}}) \propto t_{\text{w}}^{\alpha_{t_{\text{w}}}}$ with
$\alpha_{t_{\text{w}}} \simeq -1.75$ and $N(E)\text{d}E \propto
E^{\alpha_{E}}\text{d}E$ with $\alpha_{E} \simeq -1.67$, respectively. These
properties are consistent with the observations of FRB 121102.
