This note addresses the feedback robust model predictive control (FRMPC) for a category of linear parameter varying (LPV) systems with bounded rates of parameter changes. Based on the bounded rates of parameter changes and the detected current system parameters, future model variations can be described by a sequence of polytopic families with the same number of vertices. Then a FRMPC algorithm is developed. Since both the future model variations and the corresponding sequence of feedback control laws are adopted, the FRMPC can achieve high control performance. By transferring main design work to offline design, an efficient FRMPC is also developed. The recursive feasibility and closed-loop stability of the FRMPCs are proved to be guaranteed.