Summary: In this paper, we study the problem of the strong edge-coloring of Möbius ladder \(C (2n, n)\). By using a combinatorial method, we obtain the following results: \(\chi'_s (C (2n, n)) = 9\) if \(n = 3\); \(\chi'_s (C (2n, n)) = 10\) if \(n = 4\); \(\chi'_s (C (2n, n)) = 8\) if \(n = 5, 8\); \(\chi'_s (C (2n, n)) = 6\) if \(n \geq 3\) and \(n \equiv 2 \pmod 4\); \(\chi'_s (C (2n, n)) = 7\) if \(n \geq 7\) and \(n \equiv 0, 1\) or \(3 \pmod 4\).