Prediction of single-cross performance has been a major goal of plant breeders since the beginning of hybrid breeding because it is not feasible to evaluate all single-cross combinations between parental inbreds in a hybrid breeding program. Recently, simulation and experimental studies have shown great promise of genomic prediction of single-cross performance. However, further investigations are needed for optimal implementation of genomic prediction for single-cross performance. The objectives of this dissertation were to (1) examine the potential of genomic prediction of single crosses in the early stages of hybrid breeding pipeline, (2) evaluate the nonparametric models for genomic prediction of early-stage single crosses and (3) optimize the training set composition for genomic prediction of early-stage single crosses. Two different datasets consisting of 481 and 312 single crosses generated between random set of recombinant inbred lines (RILs)/doubled haploid lines (DHLs) derived from series of biparental families belonging to Iowa Stiff Stalk Synthetic (BSSS) and Non-Stiff Stalk Synthetic (NSSS) heterotic group were used. All the parental RILs/DHLs were genotyped using genotyping by sequencing approach. The accuracies of genomic prediction were substantially higher than topcross-based prediction commonly used in the early stages hybrid breeding. Moreover, genomic prediction outperformed phenotype-based prediction when only one or none of the parents of single crosses were tested. The mean genomic predictive abilities for T2, T1F, T1M, and T0 single crosses were 0.67, 0.60, 0.55, 0.46 for GY and 0.84, 0.74, 0.74, 0.63 for PH correspondingly. Genomic best linear unbiased prediction (GBLUP) and three nonparametric models namely reproducing kernel Hilbert space (RKHS), support vector regression (SVR) and neural network (NN) provided similar predictive abilities. Genetic relationship and training set (TRS) size in addition to the number of tested parents of single crosses considerably influenced the predictive abilities. Expected prediction accuracies based on prediction error variance (PEV) agreed well with empirical prediction accuracies when population structure was accounted. Genomic prediction models constructed on TRS optimized with PEV mean and coefficient of determination (CD) mean criteria provided increased predictive ability than stratified and randomly sampled TRS. Overall, the results of this study suggest that genomic prediction of early-stage single crosses with TRS optimization using PEV and CD mean criteria has great potential to redesign hybrid maize breeding and increase its efficiency.