Summary: The linear arboricity \(\text{la}(G)\) of a graph \(G\) is the minimum number of linear forests that partition the edges of \(G\). \textit{J. Akiyama} et al. [Networks 11, 69--72 (1981; Zbl 0479.05027)] conjectured that \(\big\lceil\frac{\Delta(G)}{2}\big\rceil\leq \text{la}(G)\leq\big\lceil\frac{\Delta(G)+1}{2}\big\rceil\) for any simple graph \(G\). A graph \(G\) is 1-planar if it can be drawn in the plane so that each edge has at most one crossing. In this paper, we confirm the conjecture for 1-planar graphs \(G\) with \(\Delta(G)\geq13\).