  Given a family $\{ f_{\lambda} \}_{\lambda \in \Lambda}$ of polynomial maps
of degree $d$ where $\Lambda$ is the set of parameters, a polynomial map
$f_{\lambda_0}$ is called {\it $J$-stable in $\Lambda$} if there exists a
neighborhood of $\lambda_0$ in $\Lambda$ such that for any element $\lambda$ in
the neighborhood, there exists a conjugacy between the dynamics on the Julia
sets of $f_\lambda$ and $f_{\lambda_0}$. The aim of this paper is to show that
a polynomial map $f_{\lambda_0}$ over the field $\mathbb{C}_p$ of $p$-adic
complex numbers is $J$-stable in the family of polynomial maps over
$\mathbb{C}_p$ if $f_{\lambda_0}$ is {\it immediately expanding}.
