In this paper, we show a generalized P\'{o}lya-Szeg\"{o} inequality 
for  the Hadamard product: Let $A$ and $B$ be $k\times k$-positive definite matrices 
such that $mI\leq A, B\leq MI$ for some scalars $0<m<M$. 
Then
\[
\sqrt{(A^2x,x)(B^2x,x)} \leq \ k\cdot \frac{M^2+m^2}{2Mm} (A \circ B \ x,x)
\] 
for every vector $x$, where $I$ is the identity matrix and the symbol $\circ$ 
is the Hadamard product.