Advancements in sensor technology have enabled the measurement of road profile information ahead of the vehicle. In this context, model predictive control (MPC) emerges as a viable control strategy for implementing active suspension systems, especially when equipped with road preview sensors. This preference is attributed to the ability of the MPC approach to make real-time predictions about the future behavior of the system and to accommodate constraints during the optimization process. Additionally, it is worth noting that the effectiveness of employing an inerter in passive suspension systems has been well-demonstrated in the previous research. Therefore, this study proposes an inerter-based active suspension controlled by the MPC scheme with the road preview information. To assess the efficacy of the proposed strategy, numerical simulations are conducted using a quarter car model. By comparing to the passive control and the existing MPC approaches, the advantages of the MPC with preview for performance improvement of the suspension were validated.