Schemes for predicting seismic ground motion, including real‐time prediction (earthquake early warning [EEW]), ideally should incorporate the effects of the source, path, and site amplification terms. In this study, we incorporated the path term into the numerical shake prediction scheme, a promising approach to EEW, in an effort to predict future ground motions with a heterogeneous attenuation structure. We characterized the heterogeneous attenuation structure of southwestern Japan using multiple lapse time window analysis, then incorporated that attenuation structure in a simulation of ground‐motion prediction for the largest earthquake (⁠ M w 7.0) of the 2016 Kumamoto earthquake sequence. The heterogeneous attenuation structure led to improvements over a homogeneous structure: the root mean square residuals of the predicted seismic intensities were 12% lower for predictions 10 s ahead and 15% lower for predictions 20 s ahead, suggesting that the benefit of using a heterogeneous attenuation structure is greater for longer lead times. Our results show that details of the attenuation structure should be considered to lengthen the lead time of ground‐motion predictions by the numerical shake prediction scheme.