The commutator of convolution type Calderon-Zygmund singular integral operators with rough kernels $p.v. \frac {\Omega (x)}{|x|^n}$ are studied. The authors established the $L^p\,(1>p>\infty )$ boundedness of the commutators of singular integrals and maximal singular integrals with the kernel condition which is different from the condition $\Omega \in H^1(S^{n-1}).$

N this paper the authors prove the L^2(\mathbb{R}^n) boundedness of the commutator of the singular integral operator with rough variable kernels, which is a substantial improvement and extension of some known results.