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 $xi approx -35$.
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