Summary: Let \(G\) be a graph and \(k\) a positive integer. A strong \(k\)-edge-coloring of \(G\) is a mapping \(\phi: E(G)\to \{1,2,\dots,k\}\) such that for any two edges \(e\) and \(e^\prime\) that are either adjacent to each other or adjacent to a common edge, \( \phi(e)\neq \phi(e^\prime)\). The strong chromatic index of \(G\) is the minimum integer \(k\) such that \(G\) has a strong \(k\)-edge-coloring. The edge weight of \(G\) is defined to be \(\max\{d(u)+d(v):uv\in E(G)\}\), where \(d(v)\) denotes the degree of \(v\) in \(G\). In this paper, we prove that every claw-free graph with edge weight at most 7 has strong chromatic index at most 9, which is sharp.