Precise control of the air-fuel ratio in a spark ignition (SI) engine is important to minimize emissions. The emission reduction strongly depends on the performance of the air-fuel ratio controller for the SI engine in conjunction with the Three Way Catalytic (TWC) converter. The TWC converter acts as a buffer to any variations occurring in the air-fuel ratio. It stores oxygen during a lean operation and releases the stored oxygen during a rich transient phase. The stored oxygen must be maintained close to the current storage capacity to yield maximum benefits from the TWC converter. Traditionally this is achieved using a simple PI control or a gain-scheduled PI control to address the variability in the operating conditions of the engine. This, however, does not guarantee closed-loop system stability and/or performance. In this work a model-based linear parameter varying (LPV) approach is used to design an H∞ controller. The design goal is to minimize the effect of disturbances on the air-fuel ratio and hence the relative storage level of oxygen in the TWC, over a defined operating range for the SI engine. The design method formulated in terms of Linear Matrix Inequalities (LMIs) leads to a convex optimization problem which can be efficiently solved using existing interior-point optimization algorithms. Simulations performed validate the proposed control design methodology.