Centralized control of wave energy converter (WEC) arrays for grid-scale generation can achieve higher energy production than decentralized (independent) control, due to its capability of fully exploiting mutual radiation effects. However, the state-of-the-art centralized model predictive control (CMPC) is significantly more computationally challenging than decentralized MPC (DMPC), since the number of control moves to be optimized grows in proportion to the number of WECs. In this paper, a fast CMPC controller is proposed, whose idea is to optimize only the first few control moves while rolling out future system trajectories using a fixed controller. A linear, two-degree-of-freedom (2-DoF) controller with a sea-state-dependent control coefficient tuning strategy is further proposed to serve as the rollout controller. It is shown that the proposed rollout-based CMPC (R-CMPC) can maintain almost the same energy production as conventional CMPC under a wide range of sea states, while significantly reducing the optimization dimension (in the studied case, by a factor of 6), enabling ultra-fast online computation (about 40 times faster than conventional CMPC).