Let $G$ be a finite Abelian group and $S$ be a subset of $G$. The Cayley sum graph $\operatorname{Cay}^+(G,S)$ of $G$ with respect to $S$ is a graph whose vertex set is $G$ and two vertices $g$ and $h$ are joined by an edge if and only if $g+h\in S$. In this paper, we prove some basic facts on the domination and total domination numbers of Cayley sum graphs. Then, we find the sharp bounds for domination number of $\operatorname{Cay}^+(\Bbb{Z}n,S)$, where $S=\{1,2,\ldots,k\}$ and $n,k$ are positive integers with $1\leq k\leq(n-1)/2$.