The zeroth-order general Randić index of graph $G=(V_G,E_G)$, denoted by $^0R_α(G)$, is the sum of items $(d_{v})^α$ over all vertices $v\in V_G$, where $α$ is a pertinently chosen real number. In this paper, we obtain the sharp upper and lower bounds on $^0R_α$ of trees with a domination number $γ$, in intervals $α\in(-\infty,0)\cup(1,\infty)$ and $α\in(0,1)$, respectively. The corresponding extremal graphs of these bounds are also characterized.