An explicit sufficient condition on the hypercontractivity is presented for the Markov semigroup  associated to a   class of functional stochastic differential equations.  Consequently, the semigroup $P_t$ converges exponentially to its unique invariant probability measure $/mu$ in both $L^2(/mu)$ and the totally variational norm, and it is compact in $L^2(/mu)$ for large $t>0$. This   provides a class of  non-symmetric Markov semigroups which are compact for large time but non-compact for small time. A semi-linear model which may not satisfy this sufficient condition is also investigated.