Darafsheh and Assari in [Normal edge-transitive Cayley graphs on non-abelian groups of order ۴p , where p is a prime number ,  Sci . China Math ., ۵۶ (۱) (۲۰۱۳) ۲۱۳-۲۱۹.] classified the connected normal edge transitive and ۱۲−arc-transitive Cayley graph of groups of order ۴p . In this paper we continue this work by classifying the connected Cayley graph of groups of order ۲pq , p>q are primes . As a consequence it is proved that Cay(G,S) is a ۱۲−arc-transitive Cayley graph of order ۲pq , p>q if and only if |S| is an even integer greater than ۲ , S = T