It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse-time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time-space domain dispersion-relation-based finite-difference (FD) method for visco-acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time-space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time-space domain FD method to solve the visco-acoustic wave equation in wavefield extrapolation of RTM and apply the source-normalized cross-correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco-acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable-length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution.