In this study, a linear model predictive control (MPC) approach with optimal filters is proposed for handling unmeasured disturbances with arbitrary statistics. Two types of optimal filters are introduced into the framework ofMPC to relax the assumption of integratedwhite noisemodel in existing approaches. The introduced filters are globally optimal for linear systems with unmeasured disturbances that have unknown statistics. This enables the proposed MPC to better handle disturbances without access to disturbance statistics. As a result, the effort required for disturbance modeling can be alleviated. The proposed MPC can achieve offset-free control in the presence of asymptotically constant unmeasured disturbances. Simulation results demonstrate that the proposed approach can provide an improved disturbance orejection performance over conventional approaches when applied to the control of systems with unmeasured disturbances that have arbitrary statistics. (C) 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.