  A graph $\Gamma$ is called $(G, s)$-arc-transitive if $G \le
\mathrm{Aut}(\Gamma)$ is transitive on the set of vertices of $\Gamma$ and the
set of $s$-arcs of $\Gamma$, where for an integer $s \ge 1$ an $s$-arc of
$\Gamma$ is a sequence of $s+1$ vertices $(v_0,v_1,\ldots,v_s)$ of $\Gamma$
such that $v_{i-1}$ and $v_i$ are adjacent for $1 \le i \le s$ and $v_{i-1}\ne
v_{i+1}$ for $1 \le i \le s-1$. $\Gamma$ is called 2-transitive if it is
$(\mathrm{Aut}(\Gamma), 2)$-arc-transitive but not $(\mathrm{Aut}(\Gamma),
3)$-arc-transitive. A Cayley graph $\Gamma$ of a group $G$ is called normal if
$G$ is normal in $\mathrm{Aut}(\Gamma)$ and non-normal otherwise. It was proved
by X. G. Fang, C. H. Li and M. Y. Xu that if $\Gamma$ is a tetravalent
2-transitive Cayley graph of a finite simple group $G$, then either $\Gamma$ is
normal or $G$ is one of the groups $\mathrm{PSL}_2(11)$, $M_{11}$, $M_{23}$ and
$A_{11}$. However, it was unknown whether $\Gamma$ is normal when $G$ is one of
these four groups. In the present paper we answer this question by proving that
among these four groups only $M_{11}$ produces connected tetravalent
2-transitive non-normal Cayley graphs. We prove further that there are exactly
two such graphs which are non-isomorphic and both determined in the paper. As a
consequence, the automorphism group of any connected tetravalent 2-transitive
Cayley graph of any finite simple group is determined.
