Single-step GBLUP (ssGBLUP) to obtain genomic prediction was proposed in 2009. Many studies have investigated ssGBLUP in genomic selection in animals and plants using a standard linear kernel (similarity matrix) called genomic relationship matrix (G). More general kernels should allow capturing non-additive effects as well, whereas GBLUP is based on additive gene action. In this study, we generalized ssBLUP to accommodate two non-linear kernels, the averaged Gaussian kernel (AK) and the recently developed arc-cosine deep kernel (DK). We evaluated the methodology using body weight (BW) and hen-housing production (HHP) traits, recorded on a sample of phenotyped and genotyped commercial broiler chickens. There were, thus, different ssGBLUP models corresponding to G, AK and DK. We used random replication of training (TRN) and testing (TST) layouts at different genotyping rates (20%, 40%, 60% and 80% of all birds) in three selective genotyping scenarios. The selections were genotyping the youngest individuals in the pedigree (YS), random genotyping (RS) and genotyping based on parent average (PA). Predictive abilities were measured using rank correlations between the observed and the predictive phenotypic values in TST for each random partition. Prediction accuracy was influenced by the type of kernel when a large proportion of birds was genotyped. An advantage of non-linear kernels (AK and DK) was more apparent when 60 and 80% of birds had been genotyped. For BW, the lowest rank correlations were obtained with G (0.093 ± 0.015 using RS by 20% genotyped individuals) and the highest values with DK (0.320 ± 0.016 in the PA setting with 80% genotyped individuals). For HHP, the lowest and highest rank correlations were obtained by AK with 20% and 80% genotyped individuals, 0.071 ± 0.016 (in RS) and 0.23 ± 0.016 (in PA) respectively. Our results indicated that AK and DK are more effective than G when a large proportion of the target population is genotyped. Our expectation is that ssGBLUP with AK or DK models can perform even better than G when non-additive genetic effects influence the underlying variability of complex traits.