  Let $\phi(z)=(\phi_1(z), ...,\phi_n(z))$ be a holomorphic self-map of $U^n$
and $\psi(z)$ a holomorphic function on $U^n,$ where $U^n$ is the unit polydisk
of ${\Bbb C}^n.$ Let $p\geq 0,$ $q\geq 0$, this paper gives some necessary and
sufficient conditions for the weighted composition operator $W_{\psi,\phi}$
induced by $\psi$ and $\phi$ to be bounded and compact between $p$-Bloch space
${\cal B}^p(U^n)$ and $q$-Bloch space ${\cal B}^q(U^n).$
