Abstract The dramatic advancement in genotyping technology has greatly reduced the complexity and cost of genotyping. The continuous increase in the density of marker panels is resulting in little to no improvement in the accuracy of genomic selection. Direct inversion of the genomic relationship matrix is infeasible for some livestock populations due to the excessive computational cost. In addition, most animals in genetic evaluation programs are non-genotyped. Including these animals in a genomic evaluation requires the imputation of the missing genotypes when using regression methods. To overcome these challenges, a hybrid approach is proposed. This approach fits a subset of SNP markers selected based on FST scores and a classical polygenic effect. The method was first tested using only genotyped animals and then extended to accommodate non-genotyped animals. The proposed approach was evaluated using simulated data for a trait with heritability of 0.1 and 0.4 and weaning weight in a crossbred beef cattle population. When all animals were genotyped, the hybrid approach using only 2.5% of prioritized SNPs exceeded the prediction accuracies of BayesB, BayesC, and GBLUP by more than 7%. When non-genotyped animals were incorporated, the proposed approach significantly outperformed ss-GBLUP method in terms of prediction accuracy under both simulated heritability scenarios. Although the results seem to depend on the genetic complexity of the trait, the proposed approach resulted in higher prediction accuracies than current methods. Furthermore, its computational costs in terms of CPU time and peak memory are substantially lower than the current methods.