Improving textile characteristics is the main objective of alpaca breeding. A recently developed SNP chip for alpacas could potentially be used to implement genomic selection and accelerate genetic progress. Therefore, this study aimed to compare the increase in prediction accuracy of three important fiber traits: fiber diameter (FD), standard deviation of fiber diameter (SD), and percentage of medullation (PM) in Huacaya alpacas. The data contains a total pedigree of 12,431 animals, 24,169 records for FD and SD, and 8386 records for PM and 60,624 SNP markers for each of the 431 genotyped animals of the Pacomarca Genetic Center. Prediction accuracy of breeding values was compared between a classical BLUP and a single-step Genomic BLUP (ssGBLUP). Deregressed phenotypes were predicted. The accuracies of the genetic and genomic values were calculated using the correlation between the predicted breeding values and the deregressed values of 100 randomly selected animals from the genotyped ones. Fifty replicates were carried out. Accuracies with ssGBLUP improved by 2.623%, 6.442%, and 1.471% on average for FD, SD, and PM, respectively, compared to the BLUP method. The increase in accuracy was relevant, suggesting that adding genomic data could benefit alpaca breeding programs.