This paper aims to propose an efficient network and applies it as an adaptive filter for the signal processing problems. An adaptive filter is proposed using a novel interval type-2 fuzzy cerebellar model articulation controller (T2FCMAC). The T2FCMAC realizes an interval type-2 fuzzy logic system based on the structure of the CMAC. Due to the better ability of handling uncertainties, type-2 fuzzy sets can solve some complicated problems with outstanding effectiveness than type-1 fuzzy sets. In addition, the Lyapunov function is utilized to derive the conditions of the adaptive learning rates, so that the convergence of the filtering error can be guaranteed. In order to demonstrate the performance of the proposed adaptive T2FCMAC filter, it is tested in signal processing applications, including a nonlinear channel equalization system, a time-varying channel equalization system, and an adaptive noise cancellation system. The advantages of the proposed filter over the other adaptive filters are verified through simulations.