A strong edge-coloring of a graph $G$ is an edge-coloring such that any two edges on a path of length three receive distinct colors. We denote the strong chromatic index by $χ_{s}'(G)$ which is the minimum number of colors that allow a strong edge-coloring of $G$. Erdős and Nešetřil conjectured in 1985 that the upper bound of $χ_{s}'(G)$ is $\frac{5}{4}Δ^{2}$ when $Δ$ is even and $\frac{1}{4}(5Δ^{2}-2Δ+1)$ when $Δ$ is odd, where $Δ$ is the maximum degree of $G$. The conjecture is proved right when $Δ\leq3$. The best known upper bound for $Δ=4$ is 22 due to Cranston previously. In this paper we extend the result of Cranston to list strong edge-coloring, that is to say, we prove that when $Δ=4$ the upper bound of list strong chromatic index is 22.