The short-term prediction of Earth rotation parameters (ERP) (length-of-day and polar motion) is studied up to 10 days by means of ANFIS (adaptive network based fuzzy inference system). The prediction is then extended to 40 days into the future by using the formerly predicted values as input data. The ERP C04 time series with daily values from the International Earth Rotation Service (IERS) serve as the data base. Well-known effects in the ERP series, such as the impact of the tides of the solid Earth and the oceans or seasonal variations of the atmosphere, were removed a priori from the C04 series. The residual series were used for both training and validation of the network. Different network architectures are discussed and compared in order to optimize the network solution. The results of the prediction are analyzed and compared with those of other methods. Short-term ERP values predicted by ANFIS show root-mean-square errors which are equal to or even lower than those from the other considered methods. The presented method is easy to use.