The effectiveness of sloped rolling-type seismic isolators (SRI) in seismically protecting critical equipment from malfunction and damage has already been extensively demonstrated. To prevent the isolation displacement response of SRI from reaching a threshold, passively designing a large and conservative damping force for SRI is usually required, which accordingly leads to enlarged and even unacceptable transmitted acceleration responses. That is, for seismic isolation, there is always a trade-off between minimizing acceleration and displacement responses. Previous studies have indicated that by determining the damping force applied to SRI based on the possible information provided by an earthquake early warning system and adjusting it in a semi-active control manner, its acceleration and displacement responses can be controlled more satisfactorily. However, this is based on the premise that the parameters of input excitation needed for determining the damping force are predicted promptly and accurately. Besides, among the discussed parameters, the peak velocity (PV) was most recommended. To further improve this, in this study, for the first few seconds after the arrival of primary waves (P-wave), the prediction models of PV are developed using the artificial neural network (ANN) approach. Based on the early prediction of PV as well as the proposed control law, the required damping force for SRI can be determined merely several seconds after P-wave arrival. The control performances of SRI, whose damping forces are determined using the predictions of PV at different times after P-wave arrival, are numerically examined. Through studies under a large number of conditions based on different earthquake records together with the ground motions recorded in an independent damaging earthquake event, a combination of ANN models at different, suitable times after P-wave arrival is recommended to determine the damping force applied to SRI.