  In this short paper we study $L_f^p$-Liouville property with $0<p<1$ for
nonnegative $f$-subharmonic functions on a complete noncompact smooth metric
measure space $(M,g,e^{-f}dv)$ with $\mathrm{Ric}_f^m$ bounded below for
$0<m\leq\infty$. We prove a sharp $L_f^p$-Liouville theorem when $0<m<\infty$.
We also prove an $L_f^p$-Liouville theorem when $\mathrm{Ric}_f\geq 0$ and
$|f(x)|\leq \delta(n) \ln r(x)$.
