  In higher-curvature inflation models ($R+\alpha_n R^n$), we study a
parametric preheating of a scalar field $\chi$ coupled non-minimally to a
spacetime curvature $R$ ($\xi R \chi^2$). In the case of $R^2$-inflation model,
efficient preheating becomes possible for rather small values of $\xi$, i.e.
$|\xi|< several. Although the maximal fluctuation $\sqrt{< \chi^2 >}_{max}
\approx 2 \times10^{17}$ GeV for $\xi \approx -4$ is almost the same as the
chaotic inflation model with a non-minimally coupled $\chi$ field, the growth
rate of the fluctuation becomes much larger and efficient preheating is
realized. We also investigate preheating for $R^4$ model and find that the
maximal fluctuation is $\sqrt{< \chi^2 >}_{max} \approx 8 \times 10^{16}$ GeV
for $\xi \approx -35$.
