It is difficult to model and predict satellite clock offset with conventional approaches. In this paper, an extreme learning machine (ELM) is used to predict satellite clock offset in order to improve prediction accuracy. For the problem that it is arduous to determine the hidden layer structure of ELM neural network, a new algorithm for ELM network structure design is proposed based on the good online classified characteristic of adaptive resonance theory (ART) network. The proposed algorithm employs the clustering characteristic of ART network to design the ELM network structure. The number of hidden layer nodes can be determined adaptively through the similarity comparison of input vector. The experiment results show that the ART-ELM prediction model outperforms the quadratic polynomial model and grey model remarkably.