<p>In the marine environment, seismic waves propagate as acoustic waves in seawater and elastic waves in subsea structures. Acoustic-elastic coupled interface control equations enable stable wavefield transmission and conversion, and acoustic-elastic coupled least-squares reverse time migration (LSRTM) outperforms single elastic wave methods in signal-to-noise ratio (SNR) and resolution. However, traditional gradient-based iterative algorithms for LSRTM suffer from oscillations and inadequate resolution, limiting practical application. To resolve these issues, this paper introduces the Nesterov accelerated gradient method into acoustic-elastic coupled LSRTM. First, based on the steepest descent method, a historical accumulated gradient factor is added to each iteration direction as a correction term for the next iteration. Second, the current iteration’s gradient direction and step size are updated via this optimized factor, eliminating orthogonality of consecutive descent directions and avoiding oscillation. Finally, normalized data residuals are compared against a threshold to output imaging results. Experiments show the method reduces LSRTM’s normalized residual by 16% on average and improves residual convergence efficiency by 24%.</p>