The paper presents short-term and long-term predictions of Earth rotation parameters (ERP) (Length-of-Day and polar motion) up to one year by means of ANFIS (Adaptive Network based Fuzzy Inference System). The ERP C04 time series of the International Earth Rotation and Reference Systems Service (IERS) with daily values are used as data basis. The impact of the tides of the solid Earth and the oceans and seasonal variations of the atmosphere are removed from the C04 series. The residual series are used both for training and validation of the ANFIS. For network optimization purposes, different architectures are considered. The results of the prediction are compared with those from other methods. The ERP values predicted by ANFIS have RMS errors, which are equal or even less than those from other methods. The most striking advantage of using ANFIS instead of other approaches is its significantly reduced complexity.