A star edge coloring of a graph $G$ is a proper edge coloring with no 2-colored path or cycle of length four. The star edge coloring problem is to find an edge coloring of a given graph $G$ with minimum number $k$ of colors such that $G$ admits a star edge coloring with $k$ colors. This problem is known to be NP-complete. In this paper, for a bounded treewidth graph with given maximum degree, we show that it can be solved in polynomial time.