The seasonality and randomness of wind present a significant challenge to the operation of modern power systems with high penetration of wind generation. An effective short-term wind power prediction model is indispensable to address this challenge. In this paper, we propose a combined model, i.e., a wind power prediction model based on multi-class autoregressive moving average (ARMA). It has a two-layer structure: the first layer classifies the wind power data into multiple classes with the logistic function based classification method; the second layer trains the prediction algorithm in each class. This two-layer structure helps effectively tackle the seasonality and randomness of wind power while at the same time maintaining high training efficiency with moderate model parameters. We interpret the training of the proposed model as a solvable optimization problem. We then adopt an iterative algorithm with a semi-closed-form solution to efficiently solve it. Data samples from open-source projects demonstrate the effectiveness of the proposed model. Through a series of comparisons with other state-of-the-art models, the experimental results confirm that the proposed model improves not only the prediction accuracy, but also the parameter estimation efficiency.