This paper proposes a novel hybrid approach for feature selection in two different relevant problems for marine energy applications: significant wave height (H) and wave energy flux (P) prediction. Specifically, a hybrid Grouping Genetic Algorithm - Extreme Learning Machine approach (GGA-ELM) is proposed, in such a way that the GGA searches for several subsets of features, and the ELM provides the fitness of the algorithm, by means of its accuracy on H or P prediction. Since the GGA was specifically created for problems involving a number of groups, the proposed algorithm may be used to evolve different groups of features in parallel, which may improve the performance of the predictions obtained. After the feature selection process with the GGA-ELM, the final results are given by an ELM and also by a Support Vector Machine, both working on the best GGA groups obtained. The performance of the proposed system has been tested in a real problem of H and P prediction at the Western coast of the USA, obtaining good results.