Cotton supplies a great majority of natural fiber for the global textile industry. The negative correlation between yield and fiber quality has hindered breeders’ ability to improve these traits simultaneously. A multi-parent advanced generation inter-cross (MAGIC) population developed through random-mating of multiple diverse parents has the ability to break this negative correlation. Genotyping-by-sequencing (GBS) is a method that can rapidly identify and genotype a large number of single nucleotide polymorphisms (SNP). Genotyping a MAGIC population using GBS technologies will enable us to identify marker-trait associations with high resolution. An Upland cotton MAGIC population was developed through random-mating of 11 diverse cultivars for five generations. In this study, fiber quality data obtained from four environments and 6071 SNP markers generated via GBS and 223 microsatellite markers of 547 recombinant inbred lines (RILs) of the MAGIC population were used to conduct a genome wide association study (GWAS). By employing a mixed linear model, GWAS enabled us to identify markers significantly associated with fiber quantitative trait loci (QTL). We identified and validated one QTL cluster associated with four fiber quality traits [short fiber content (SFC), strength (STR), length (UHM) and uniformity (UI)] on chromosome A07. We further identified candidate genes related to fiber quality attributes in this region. Gene expression and amino acid substitution analysis suggested that a regeneration of bulb biogenesis 1 (GhRBB1_A07) gene is a candidate for superior fiber quality in Upland cotton. The DNA marker CFBid0004 designed from an 18 bp deletion in the coding sequence of GhRBB1_A07 in Acala Ultima is associated with the improved fiber quality in the MAGIC RILs and 105 additional commercial Upland cotton cultivars. Using GBS and a MAGIC population enabled more precise fiber QTL mapping in Upland cotton. The fiber QTL and associated markers identified in this study can be used to improve fiber quality through marker assisted selection or genomic selection in a cotton breeding program. Target manipulation of the GhRBB1_A07 gene through biotechnology or gene editing may potentially improve cotton fiber quality.