  Let $A_{m,n}$ be the tensor product of the 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 $A_{m,n}$. In this paper, we classify the non-trivial
simple bounded weight $W_{m,n}$ modules with respect to the standard Cartan
algebra of $W_{m,n}$. Any such module is a simple quotient of a tensor module
$F(P,L(V_1\otimes V_2))$ for a simple weight module $P$ over the Weyl
superalgebra $\mathcal K_{m,n}$, a finite-dimensional simple $\gl_m$-module
$V_1$ and a simple bounded $\gl_n$-module $V_2$.
