In vehicle active suspension design, it is desirable to improve performance criteria, such as ride comfort and road holding, subject to constraints on some states and control input. To tackle this constrained optimization problem, an offline robust model predictive control (RMPC) using linear matrix inequalities (LMIs) is proposed. In conventional model predictive control (MPC), an optimization problem is solved at each sampling interval, which might lead to task overrun and hence could prevent its real-time implementation. The proposed offline RMPC approach overcomes the problem by offline optimizations prior to implementation. Moreover, it is extended to take account of parameter uncertainties. To evaluate the effectiveness of the proposed approach, it is applied to a quarter-car suspension system with structured bounded uncertainties. Comparative simulation results show that the presented offline RMPC is much faster than both online RMPC and classic MPC approaches, yet with a competitive robust performance. In addition, simulation results with different road profiles endorse independence of the proposed offline RMPC from road excitations, as well as its efficiency to deal with shocks and vibrations.