  For a $k$-graph $\mathcal{F}\subset \binom{[n]}{k}$, the clique number of
$\mathcal{F}$ is defined to be the maximum size of a subset $Q$ of $[n]$ with
$\binom{Q}{k}\subset \mathcal{F}$. In the present paper, we determine the
maximum number of edges in a $k$-graph on $[n]$ with matching number at most
$s$ and clique number at least $q$ for $n\geq 8k^2s$ and for $q \geq (s+1)k-l$,
$n\leq (s+1)k+s/(3k)-l$. Two special cases that $q=(s+1)k-2$ and $k=2$ are
solved completely.

Combinatorics