Abstract: The vertex-distinguishing star edge chromatic number of $G$, denoted by $\chi'_{\rm vds}{(G)}$, is the minimum number of colors in a vertex-distinguishing star edge coloring of $G$. The vertex-distinguishing star edge colorings of some particular graphs were obtained. Furthermore, if $G(V,E)$ is a graph with $\delta\geqslant 5$, and $n\leqslant  \Delta^7$, then $\chi'_{\rm vds}{(G)}\leqslant 14\Delta^2$, where $n$ is the order of $G$,
$\delta(G)$ is the minimum degree of $G$, and $\Delta(G)$ is the maximum\linebreak degree of $G$.

Key words: vertex-distinguishing edge chromatic number, vertex-distinguishing star edge chromatic number, probability method