In this paper, a new data-driven method for designing robust controllers is proposed for systemswith sector-bounded nonlinearities and multimodel uncertainties. The results from the circle criterion are used to generate necessary and sufficient convex constraints that guarantee the stability of the closed-loop system. The main feature of the proposed approach is that only the frequency response data of the linear part of the system is used for guaranteeing the stability of the closed-loop nonlinear system. Additionally, a convex optimization problem is formulated to ensure H-infinity performance with respect to the fundamental component of a sector-bounded nonlinearity. The case study illustrates how the proposed method can be used to control uncertain systems that are subject to sector-bounded nonlinearities.