Genomic selection can be considered as an effective tool for developing breeding programs in American mink. However, the genetic gains for economically important traits can be influenced by the accuracy of genomic predictions. The objective of this study was to investigate the prediction accuracies of traditional best linear unbiased prediction (BLUP), multi-step genomic BLUP (GBLUP) and single-step GBLUP (ssGBLUP) methods in American mink using simulated data with different levels of heritability, marker density, training set (TS) sizes and selection designs based on either phenotypic performance or estimated breeding values (EBVs). Under EBV selection design, the accuracy of BLUP predictions was increased by 38% and 44% for h2 = 0.10, 27% and 29% for h2 = 0.20, and 5.8% and 6% for h2 = 0.50 using GBLUP and ssGBLUP methods, respectively. Under phenotypic selection design, the accuracies of prediction by ssGBLUP method were 11.8% and 15.4% higher than those obtained by GBLUP for heritability of 0.10 and 0.20, respectively. However, the efficiency of ssGBLUP and GBLUP was not influenced by selection design at higher level of heritability (h2 = 0.50). Furthermore, higher selection intensity increased the bias of predictions in both pedigree-based and genomic evaluations. Regardless of selection design, TS sizes for GBLUP and ssGBLUP methods should be at least 3000 to achieve more accuracy than using BLUP for heritability of 0.50 and marker density of 10k and 50k. Overall, more accurate predictions were obtained using ssGBLUP method particularly for lowly heritable traits and low density of markers. Our results indicated that TS sizes should be optimized in accordance with heritability level, marker density, selection design and prediction method for genomic selection in American mink. The results provided an initial framework for designing genomic selection in mink breeding programs.