This paper extends the LTI anti-windup compensator scheme proposed in  to linear parameter-varying (LPV) systems. Following the MRAW concept, the dynamical part of the compensator is formed by the exact copy of the plant. The design procedure is thus simplified to the construction of a parameter-dependent state feedback, which stabilizes the plant's copy and determines the performance and the domain of applicability of the compensator. To decrease the conservatism, the presented method applies parameter-dependent Lyapunov function and embeds the saturation (dead-zone) in a parameter-dependent sector. The design is formulated as an LMI-based convex optimization problem. The paper also investigates the possibility of eliminating certain free variables in order to reduce the complexity of the synthesis procedure. It is shown that an elimination procedure similar to that in  can be carried out, but with LPV systems the reconstruction of the compensator gain is not so straightforward. To overcome the difficulty a novel method is proposed, which is based on a closed formula parameterizing all solutions of the synthesis LMIs. Both of the fully parameterized and the reduced complexity syntheses are presented and their properties are analyzed. The applicability of the methods is demonstrated on a simple LPV plant.