For a graph $G$, let ${\cal D}(G)$ be the set of all strong orientations of $G$. The orientation number of $G$ is $\overrightarrow{d}(G)=\min\{d(D)|D\in {\cal D}(G)\}$,where $d(D)$ denotes the diameter of the digraph $D$. In this paper, we determine the orientation number for some complete tripartite graphs.