Wave energy flux is a critical index of available wave energy in a region. The short-term wave energy flux prediction is conducive to implementing marine energy generation management. Due to the high degree of nonlinearity in the time series, it is challenging to achieve the accurate prediction of the short-term wave energy flux. The existing prediction models usually only focus on the prediction accuracy without considering the prediction stability. This paper presents hybrid support vector models combining a multi-objective optimizer and data denoising for short-term wave energy flux prediction. The proposed models are tested on the hourly wave energy flux data from November 2014 to January 2015 at the South Energy Test Site in the United States. The results indicate that: (1) The model combining ensemble empirical mode decomposition with multi-objective grey wolf optimizer and support vector machine has the highest prediction accuracy and stability in the case study. The mean absolute percentage error and standard deviation of the percent error are 1.95% and 2.46%, respectively; (2) The data decomposition method improves the radial basis function neural network's prediction accuracy and stability, but has a negative impact on some predictors, such as extreme gradient boosting and random forest; (3) The optimizer does not necessarily have a positive effect on the accuracy and stability of the predictor; (4) The prediction accuracy and stability of the multi-objective optimization hybrid model are higher than that of the single-objective optimization model.