Abstract: In this paper, the authors discuss the$(H^{1}(\rr^{n}),L^{\frac{n}{n-\alpha},\infty}(\rr^{n}))$
boundedness of the multilinear operator related to fractional integral with rough kernel
\[T_{\Omega,\alpha}^{A}(f)(x)={\rm p.v.}\int_{R^{n}}P_{m}(A;x,y)
\frac{\Omega(x-y)}{|x-y|^{n-\alpha+m-1}}f(y){\rm d}y.\]

Key words: Fractional integral, Commutator, Multilinear operator