We estimated ground motions at 12 selected sites in the Kachchh rift basin of Gujarat in the western peninsular shield area of India, where the damaging 1956 Anjar earthquake (Mw 6.0) was experienced. The ground motions are estimated by applying the empirical Green’s function approach using an earthquake of Mw 4.5, which occurred on the inferred rupture plane of the Anjar earthquake with a nearly similar fault mechanism. The estimated peak ground acceleration (PGA) varies between 114 and 22 cm/s2 at these sites, located at distances of 21–127 km from the epicenter, respectively. The maximum accelerations are correlated with the modified Mercalli intensity reported for the Anjar earthquake using the empirical relationship between the PGA and intensity. At most of the sites, the level of acceleration could explain the reported damage. At a few sites, the instrumental intensity estimated using the acceleration values obtained from the synthesis is larger than the felt intensity. The ground‐motion prediction equation (GMPE) developed for the region estimates the maximum PGA near the epicenter area in the 250–300 cm/s2 range, and the acceleration obtained by our analysis is found to be closer to the predicted acceleration obtained by GMPE. Our analysis assesses the level of ground motion that was experienced during the 1956 Anjar earthquake fairly well and corroborates that reasonable prediction of the ground motion of a historical earthquake is achievable, if strong‐motion recordings are available from the rupture plane of the historical earthquake.