  For a finite group $G$ and a positive integer $n$, let $G(n)$ be the set of
all elements in $G$ such that $x^{n}=1$. The groups $G$ and $H$ are said to be
of the same (order) type if $G(n)=H(n)$, for all $n$. The main aim of this
paper is to show that if $G$ is a finite group of the same type as Suzuki
groups $Sz(q)$, where $q=2^{2m+1}\geq 8$, then $G$ is isomorphic to $Sz(q)$.
This addresses the well-known J. G. Thompson's problem (1987) for simple
groups.
