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Genomic prediction has been applied to various species of plants and livestock to enhance breeding efficacy. Neural networks including deep neural networks are attractive candidates to predict phenotypic values. However, the properties of neural networks in predicting non-additive effects have not been clarified. In this simulation study, factors affecting the prediction of genetic values associated with gene interactions (i.e., epistasis) were investigated using multilayer perceptron. The results suggested that (1) redundant markers should be pruned, although markers in LD with QTLs are less harmful, (2) predicting epistatic genetic values with neural networks in real populations would be infeasible using training populations of 1000 samples, (3) neural networks with two or fewer hidden layers and a sufficient number of units per hidden layer would be useful, particularly when a certain number of interactions is involved, and (4) neural networks have greater capability to predict epistatic genetic values than random forests, although neural networks are more sensitive to training population size and the level of epistatic genetic variance. These lessons also would be applicable to other regression problems in which interactions between explanatory variables are expected, e.g., gene-by-environment interactions.