Let $G$ be a finite group. An automorphism $\alpha$ of $G$ is called an $IA$-auto\-mor\-phism if $x^{-1}x^{\alpha}\in G'$ for all $x\in G$. The set of all $IA$-automorphisms of $G$ is denoted by $Aut^{G'}(G)$. A group $G$ is called semicomplete if and only if $Aut^{G'}(G)=Inn(G)$. In this paper, we obtain certain conditions on a finite $p$-group to be semicomplete.