The purpose of this study was determining, by simulation, whether (single-step) GBLUP is useful for genomic analyses when causative Quantitative Trait Nucleotides (QTNs) are known. Simulations included 180k animals in 11 generations. Simulated population mimicked a cattle population with weak selection intensity (Ne ~200). Phenotypes were available for animals in generations 6–10. Genotypes were available for 24k parents and 5k young animals in generation 11, and included 60k regular SNPs in 10 chromosomes, with genetic variance fully accounted for by 100 or 1,000 biallelic QTN, with effected sampled from a gamma distribution with shape parameter equal 0.4. LD (r²) between SNPs was in average 0.63 across generations and chromosomes, Genomic relationship matrices were computed from a) unweighted regular SNP, b) unweighted regular SNP and + QTN, c) regular SNP with variances from GWA, d) unweighted regular SNP and QTN with known variances, e) as before but only using 10% of the largest QTNs, and f) using only QTNs with known variances. Accuracies for the 11th generation were computed by BLUP and ssGBLUP. To ensure full rank, raw genomic relationship matrices (GRM) were blended with 1% or 5% of numerator relationship matrix, or 1% of the identity matrix. Rank of GRM with 100 QTN as determined by the number of eigenvalues explaining 90% variation in GRM was 8,497 for unweighted GRM, increased to 9,553 after blending,decreased to 4,054 with weighted GRM and 10% QTN included, and was 76 when only causative QTNs were used. The accuracy for the last genotyped generation with BLUP was 0.32. For ssGBLUP, that accuracy increased to 0.49 with a regular GRM, to 0.53 after adding unweighted QTN, to 0.63 when QTN variances were estimated, and to 0.89 when QTN variances were assumed known. When GRM was constructed from QTNs only, the accuracy was 0.95 with 5% blending rising to 0.99 with 1% blending. Accuracies assuming 1000 QTN were generally lower, with a similar trend. Accuracies using the APY inverse were equal or higher than those with a regular inverse. The rank of weighted GRM is between the rank of unweighted GRM and that computed with causative SNP only. Single-step GBLUP can account for causative SNP when variances of causative QTN are known.