This talk is based on the joint work with Dr. Yaohui Xue(薛耀辉). Let $A_{m,n}$ be the tensor product of the Laurient polynomial algebra in m even variables and the exterior algebra in n odd variables over the complex field $\C$, and the Witt superalgebra $W_{m,n}$ be the Lie superalgebra of superderivations of $A_{m,n}$. We classify the simple weight $W_{m,n}$ modules with finite-dimensional weight spaces with respect to the standard Cartan algebra of $W_{m,0}$. Every such module is either a simple quotient of a tensor module or a module of highest weight type.

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