This study sought to develop a genetic map of cassava based on 91 progenies derived from a cross between “Rayong 60” (R60) and “Piroon 1” (PR1) cultivars. A total of 4,515 simple sequence repeat (SSR) primer pairs were screened against the parental lines and six progenies resulting in 656 informative polymorphic markers, which were then used to genotype the F1 population. A total of 314 linked SSR loci were identified that were distributed across 40 linkage groups (LGs) at a logarithm of the odds (LOD) score of 4.0. The total distance of the linkage map was 2,026.68 cM with an average of 13.85 cM between markers and 7.85 loci per LG. The SSR loci on each LG were categorized into the 18 chromosomes of the cassava genome. Two major quantitative trait loci (QTL) and one minor QTL controlling first branch height (FBH) were detected with phenotypic variability explained (PVE) ranging from 10.2–18.9% and 8.2%, respectively. In addition, two major QTL for plant height (PH) with PVE ranging from 16.5–24.3% were detected in the F1 population. The QTL controlling PH and FBH detected in this study will be useful for future identification of QTL and genes underlying economically important traits to accelerate molecular breeding of cassava variety improvement via marker-assisted selection.