An offset-free controller is one that drives controlled outputs to their set-point values at the steady state. In the literature, conditions for offset-free linear model predictive control are given for combined estimator (for both the artificial disturbance and system state), steady-state target calculation, and dynamic controller. In the presence of steady-state target calculation, the framework for MPC is called the double-layered MPC. Usually, the offset-free property of the double-layered MPC is obtained under the assumption that the system is asymptotically stable. This paper discusses on the dynamic stability property which has been rarely considered in the literature of double-layered MPC.