We developed a fast method for spatially highly detailed nonlinear viscoelastic crustal deformation analysis by a combination of a data-driven method and a multi-grid solver. Here, highly accurate estimations of the solution of the next time step are obtained using a data-driven predictor based on the history of past solutions, which reduces the number of iterative solver iterations and thus reduces the computation cost. Although this method has been shown to enable fast linear viscoelastic analysis, its validity has not been confirmed for nonlinear viscoelastic problems. Numerical experiments have shown that the data-driven method reduces the number of iterations by 3.35-fold. To achieve further acceleration, we introduced a multi-grid solver capable of efficiently solving large systems of equations. The proposed combination of the data-driven method and multi-grid solver is applied to nonlinear viscoelastic crustal deformation analysis of the Nankai Trough region, and it is shown that the proposed method achieved a 15.1-fold speedup, which enabled many large-scale crustal deformation simulations within reasonable computational costs. The fast nonlinear viscoelastic analysis of spatially highly detailed crustal structure models enabled by this study is expected to contribute to the advance of interplate state estimation.