It is of significance to discover genes related to fiber quality and yield traits and tightly linked markers for marker-assisted selection (MAS) in cotton breeding. In this study, 188 F8 recombinant inbred lines (RILs), derived from a intraspecific cross between HS46 and MARCABUCAG8US-1-88 were genotyped by the cotton 63K single nucleotide polymorphism (SNP) assay. Field trials were conducted in Sanya, Hainan Province, during the 2014–2015 cropping seasons under standard conditions. Results revealed significant differences (P < 0.05) among RILs, environments and replications for fiber quality and yield traits. Broad-sense heritabilities of all traits including fiber length, fiber uniformity, micronaire, fiber elongation, fiber strength, boll weight, and lint percentage ranged from 0.26 to 0.66. A 1784.28 cM (centimorgans) linkage map, harboring 2618 polymorphic SNP markers, was constructed, which had 0.68 cM per marker density. Seventy-one quantitative trait locus (QTLs) for fiber quality and yield traits were detected on 21 chromosomes, explaining 4.70∼32.28% phenotypic variance, in which 16 were identified as stable QTLs across two environments. Meanwhile, 12 certain regions were investigated to be involved in the control of one (hotspot) or more (cluster) traits, mainly focused on Chr05, Chr09, Chr10, Chr14, Chr19, and Chr20. Nineteen pairs of epistatic QTLs (e-QTLs) were identified, of which two pairs involved in two additive QTLs. These additive QTLs, e-QTLs, and QTL clusters were tightly linked to SNP markers, which may serve as target regions for map-based cloning, gene discovery, and MAS in cotton breeding.