It has become increasingly clear from systems biology arguments that interaction and non-linearity play an important role in genetic regulation of phenotypic variation for complex traits. Marker-assisted prediction of genetic values assuming additive gene action has been widely investigated because of its relevance in artificial selection. On the other hand, it has been less well-studied when non-additive effects hold. Here, we explored a nonparametric model, radial basis function (RBF) regression, for predicting quantitative traits under different gene action modes (additivity, dominance and epistasis). Using simulation, it was found that RBF had better ability (higher predictive correlations and lower predictive mean square errors) of predicting merit of individuals in future generations in the presence of non-additive effects than a linear additive model, the Bayesian Lasso. This was true for populations undergoing either directional or random selection over several generations. Under additive gene action, RBF was slightly worse than the Bayesian Lasso. While prediction of genetic values under additive gene action is well handled by a variety of parametric models, nonparametric RBF regression is a useful counterpart for dealing with situations where non-additive gene action is suspected, and it is robust irrespective of mode of gene action.