  In this paper we introduce and study a type of Cayley graph -- subnormal
Cayley graph. We prove that a subnormal 2-arc transitive Cayley graph is a
normal Cayley graph or a normal cover of a complete bipartite graph
$K_{p^d,p^d}$ with $p$ prime. Then we obtain a generic method for constructing
half-symmetric (namely edge transitive but not arc transitive) Cayley graphs.
