Feed conversion efficiency (FCE) is an economically crucial trait in fish, however, little progress has been made in genetics and genomics for this trait because phenotypes of the trait are difficult to measure. In this study, we constructed a high-density and high-resolution genetic linkage map with 28,416 SNP markers for common carp (Cyprinus carpio) based on high throughput genotyping with the carp 250K single nucleotide polymorphism (SNP) array in a full-sib F1 family of mirror carp (Cyprinus carpio) consisting of 141 progenies. The linkage map contained 11,983 distinct loci and spanned 3,590.09 cM with an average locus interval of 0.33 cM. A total of 17 QTL for the FCE trait were detected on four LGs (LG9, LG20, LG28, and LG32), explaining 8.9–15.9% of the phenotypic variations. One major cluster containing eight QTL (qFCE1-28, qFCE2-28, qFCE3-28, qFCE4-28, qFCE5-28, qFCE6-28, qFCE7-28, and qFCE8-28) was detected on LG28. Two clusters consisting of four QTL (qFCE1-32, qFCE2-32, qFCE3-32, and qFCE4-32) and three QTL (qFCE1-20, qFCE2-20, and qFCE3-20) were detected on LG32 and LG20, respectively. Nine candidate genes (ACACA, SCAF4, SLC2A5, TNMD, PCDH1, FOXO, AGO1, FFAR3, and ARID1A) underlying the feed efficiency trait were also identified, the biological functions of which may be involved in lipid metabolism, carbohydrate metabolism, energy deposition, fat accumulation, digestion, growth regulation, and cell proliferation and differentiation according to GO (Gene Ontology). As an important tool, high-density and high-resolution genetic linkage maps play a crucial role in the QTL fine mapping of economically important traits. Our novel findings provided new insights that elucidate the genetic basis and molecular mechanism of feed efficiency and the subsequent marker-assisted selection breeding in common carp.