The fatty acid composition of meat, which affects both its quality and the consumer's health, is a complex trait influenced by genetic and environmental factors. Identification of the genes influencing the fatty acid composition of meat is very important for the selection and breeding of chickens with desirable and healthier fatty acid profiles. The objective of this study was to identify functional candidate genes for fatty acid profiles of the breast meat of the Korean native chicken-red-brown line (KNC-R) through genome-wide association studies. We genotyped 382 KNC-R chickens (190 males, 192 females) using the Illumina chicken 60K single nucleotide polymorphism (SNP) chip (Illumina, San Diego, CA, USA), and association tests were performed by mixed linear model in the Genome-wide Complex Trait Analysis (GCTA) software, based on mixed linear model analysis-leave-one-chromosome-out (MLMA-LOCO). We detected one SNP each on chromosomes 2 (rs13667281), 10 (rs14011157), and 22 (rs10731996) that were significantly (p < 0.05) associated with nervonic (C24:1), linoleic (C18:2), and eicosadienoic (C20:2) acids, respectively. We found 13 protein-coding genes related to lipid metabolism, including IGF2BP3, GPNMB, NPY, OSBPL3, IL6, NR2F2, GPAT4, NKX6-3, ANK1, SFRP1, ERLIN2, STAR, and PPP1R3E. Interestingly, two candidate genes (GPNMB and SFRP1) were reported to regulate the expression of genes known to be involved in fatty acid synthesis, such as the FASN, ACACA, ACLY, ELOVL, and SCD genes. Identification of functional candidate genes for fatty acid profiles might facilitate the selection and breeding of chickens with desirable and healthier fatty acids.