The authors proposed a symplectic stereo-modeling method (SSM) in the Birkhoffian dynamics and apply it to the visco-acoustic least-squares reverse time migration (LSRTM). The SSM adopts stereo-modeling operator in space and symplectic Runge-Kutta scheme in time, resulting in great ability in suppressing numerical dispersion and long-time computing. These advantages are further confirmed by numerical dispersion analysis, long-time computation test and computational efficiency comparison. After these theoretical analyses and experiments, acoustic and visco-acoustic LSRTM are tested and compared between SSM method and the conventional symplectic method (CSM) using the fault and marmousi models. Meanwhile, dynamic source encoding and exponential decay moving average gradients method are adopted to reduce the computation cost and improve the convergence rate. The imaging results show that LSRTM based on visco-acoustic wave equations effectively takes into account the influence of viscosity can therefore compensate for the amplitude attenuation. Besides, SSM method not only has high numerical accuracy and computational efficiency, but also performs effectively in LSRTM.