Remote driving, as a backup system for automated vehicles, can play a vital role in their commercialization. However, delay is one of the major challenges in the practical application of remote driving. It not only degrades the stability of remote driven vehicles (RDVs) but also introduces delayed driving feedback, such as motion cueing feedback, to remote drivers. This can result in an unpleasant driving experience. This study proposes a square root cubature Kalman filter-based predictor (SRCKP) to compensate for driving feedback delays in remote driving. The SRCKP reduces the limitations of both model-based and model-free predictors (MFPs). Additionally, this article presents an overshoot compensator to address the overshoot problem associated with traditional MFPs. Furthermore, a packet loss predictor (PLP) is designed to mitigate the influence of packet loss during data transmission. Both simulation and hardware-in-the-loop (HIL) experiments during comprehensive driving scenarios are conducted to verify the effectiveness and robustness of the proposed method. The findings indicate that, compared with MFPs, the SRCKP reduces the L₂-norm error by up to 81.2% in simulations and by up to 54.0% in HIL experiments for the best-case conditions.