  In this paper we consider $L^p$ boundedness of some commutators of Riesz
transforms associated to Schr\"{o}dinger operator $P=-\Delta+V(x)$ on
$\mathbb{R}^n, n\geq 3$. We assume that $V(x)$ is non-zero, nonnegative, and
belongs to $B_q$ for some $q \geq n/2$. Let $T_1=(-\Delta+V)^{-1}V,\
T_2=(-\Delta+V)^{-1/2}V^{1/2}$ and $T_3=(-\Delta+V)^{-1/2}\nabla$. We obtain
that $[b,T_j] (j=1,2,3)$ are bounded operators on $L^p(\mathbb{R}^n)$ when $p$
ranges in a interval, where $b \in \mathbf{BMO}(\mathbb{R}^n)$. Note that the
kernel of $T_j (j=1,2,3)$ has no smoothness.
