  In this paper, we are interested in the numerical solutions of stochastic
functional differential equations (SFDEs) with {\it jumps}. Under the global
Lipschitz condition, we show that the $p$th moment convergence of the
Euler-Maruyama (EM) numerical solutions to SFDEs with jumps has order $1/p$ for
any $p\ge 2$. This is significantly different from the case of SFDEs without
jumps where the order is 1/2 for any $p\ge 2$. It is therefore best to use the
mean-square convergence for SFDEs with jumps. Consequently, under the local
Lipschitz condition, we reveal that the order of the mean-square convergence is
close to 1/2, provided that the local Lipschitz constants, valid on balls of
radius $j$, do not grow faster than $\log j$.
