High density genetic linkage maps are essential for QTL fine mapping, comparative genomics and high quality genome sequence assembly. In this study, we constructed a high-density and high-resolution genetic linkage map with 28,194 SNP markers on 14,146 distinct loci for common carp based on high-throughput genotyping with the carp 250 K single nucleotide polymorphism (SNP) array in a mapping family. The genetic length of the consensus map was 10,595.94 cM with an average locus interval of 0.75 cM and an average marker interval of 0.38 cM. Comparative genomic analysis revealed high level of conserved syntenies between common carp and the closely related model species zebrafish and medaka. The genome scaffolds were anchored to the high-density linkage map, spanning 1,357 Mb of common carp reference genome. QTL mapping and association analysis identified 22 QTLs for growth-related traits and 7 QTLs for sex dimorphism. Candidate genes underlying growth-related traits were identified, including important regulators such as KISS2, IGF1, SMTLB, NPFFR1 and CPE. Candidate genes associated with sex dimorphism were also identified including 3KSR and DMRT2b. The high-density and high-resolution genetic linkage map provides an important tool for QTL fine mapping and positional cloning of economically important traits, and improving common carp genome assembly.