Abstract: A new model predictive controller ABRMPC is presented for constrained linear system with bounded additive perturbation. On the one hand, by introducing input amplitude decaying aggregation strategy, the number of optimization variables at every time is greatly reduced so that the on-line computation is simplified. On the other hand, having taken into account the perturbation at each time, some new state constraints are obtained and thus the state of the real system is kept in the original constraint domain. The paper emphasizes on how to get the feasible solution at next time and gives the condition that the decaying coefficient should satisfy. When time goes to infinite, it is proved that the system input becomes zero and the controller drives the system state to approach the invariant set. It is concluded that the controlled system is robustly stable. The conclusions are finally verified through a simulation example.