This paper concerns with adaptive gain scheduled H∞ control of LPV systems with nonlinear components. The plants in this manuscript are polytopic LPV systems with nonlinear elements, but the scheduled parameters and nonlinear elements are not known a priori, and thus, the conventional gain-scheduled control strategy cannot be applied. In the proposed adaptive control schemes, the current estimates of the scheduled parameters and nonlinear elements are fed to the controllers to stabilize the plants and to attain H∞ control performance adaptively. The neural network approximators are introduced to obtain the estimates of the nonlinear elements, and the stabilizing signals are added to suppress approximation errors and algorithmic errors included in the neural network structures and to regulate the effects of time-varying components and estimation errors of scheduled parameters and layer weights. Those additional signals are derived from another H∞ control problem.