The linear 2-arboricity la2(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose component trees are paths of length at most 2. In this paper, we prove that if G is a 1-planar graph with maximum degreeΔ, then la2(G)≤[(Δ+1)]/2]+7. This improves a known result of Liu et al. (2019) that every 1-planar graph G has la2(G)≤[(Δ+1)/2]+14. We also observe that there exists a 7-regular 1-planar graph G such that la2(G)=6=[(Δ+1)/2]+2, which implies that our solution is within 6 from optimal.