Mung bean ( Vigna radiata L.) is an important but understudied food legume in Asia and now worldwide. Genetic studies may help to accelerate the exploitation of new genes for breeding in this crop. Here, we used a recombination inbred line population to construct an SNP genetic linkage map by genome sequencing technology. We obtained 21,508 high-quality SNP markers integrated into 1,946 bin markers that were mapped onto 11 linkage groups (LGs) with 99–258 bin markers per LG. The total genetic length of the map was 1060.2 cM (38.76–168.03 cM per LG), with an average distance between markers of 0.54 cM. However, there were 18 gaps >5 cM, distribution on LG1, 3, 5, 7, and 9. Gene mapping for lobed and indented leaflets was conducted using the map. A major quantitative trait locus (QTL) associated with indented leaflets was detected on chromosome 10, with phenotypic variation explained (PVE) values of 39.7% and 45.4% under two different environments. Several QTLs for lobed leaflets were detected and most of them were tightly linked together on Chromosome 3. However, only one major QTL, which explained the largest phenotypic variation (27.7–69.5%), was stably detected under two different environments using both R and Q methods. In the two main stable QTLs regions on chromosomes 3 and 10, candidate genes for regulating the molecular mechanism of different leaflet shapes were detected by functional annotation. The overlap of major QTLs under different environments indicated that the present map would be good enough for precisely mapping genes, and both the QTL analysis and gene prediction were useful for investigating the mechanism of leaf development in mung bean or legumes.