  Let $h\geq 2$ and $A=\{a_0,a_1,\ldots,a_{k-1}\}$ be a finite set of integers.
It is well-known that $\left|hA\right|=hk-h+1$ if and only if $A$ is a $k$-term
arithmetic progression.
  In this paper, we give some nontrivial inverse results of the sets $A$ with
some extrema the cardinalities of $hA$.
