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Squash (<i>Cucurbita moschata</i>) displays wide morphological and genetic variations; however, limited information is available regarding the genetic loci of squash that control its agronomic traits. To obtain basic genetic information for <i>C. moschata</i>, an F₂ population was prepared derived from a cross between the Vietnamese cultivar ‘Bí Hồ Lô TN 6 (TN 6)’ and the Japanese cultivar ‘Shishigatani’, and flowering and fruit traits were examined. Overall, the traits showed a continuous distribution in the F₂ population, suggesting that they were quantitative traits. A linkage map was constructed based on simple sequence repeat and restriction site-associated DNA (RAD) markers to detect quantitative trait loci (QTLs). Twelve QTLs for flowering and fruit traits, as well as one phenotypic trait locus, were successfully localized on the map. The present QTLs explained the phenotypic variations at a moderate to relatively high level (16.0%–47.3%). RAD markers linked to the QTLs were converted to codominant cleaved amplified polymorphic sequence (CAPS) and derived CAPS markers for the easy detection of alleles. The information reported here provides useful information for understanding the genetics of <i>Cucurbita</i> and other cucurbit species, and for the selection of individuals with ideal traits during the breeding of <i>Cucurbita</i> vegetables.