  A subgroup $H$ of a finite group $G$ is said to satisfy $\Pi$-property in $G$
if for every chief factor $L/K$ of $G$, $|G/K:N_{G/K}(HK/K\cap L/K)|$ is a
$\pi(HK/K\cap L/K)$-number. A subgroup $H$ of $G$ is called to be
$\Pi$-supplemented in $G$ if there exists a subgroup $T$ of $G$ such that
$G=HT$ and $H\cap T\leq I\leq H$, where $I$ satisfies $\Pi$-property in $G$. In
this paper, we investigate the structure of a finite group $G$ under the
assumption that some primary subgroups of $G$ are $\Pi$-supplemented in $G$.
The main result we proved improves a large number of earlier results.
