  Let $X$ be an algebraic subvariety of $\mathbb C^n$ and $\bar X$ be its
closure in $\mathbb P^n.$ In their paper \cite{CGZ} Coman-Guedj-Zeriahi proved
that any plurisubharmonic function with logarithmic growth on $X$ extends to a
plurisubharmonic function with logarithmic growth on $\mathbb C^n$ when the
germs $(\bar X,a)$ in $\mathbb P^n$ are irreducible for all $a\in \bar
X\setminus X.$ In this paper we consider $X$ for which the germ $(\bar X,a)$ is
reducible for some $a\in \bar X\setminus X$ and we give a necessary and
sufficient condition for $X$ so that any plurisubharmonic function with
logarithmic growth on $X$ extends to a plurisubharmonic function with
logarithmic growth on $\mathbb C^n.$
