Pistachio is one of the most commercially important nut trees in the world. To characterize the genetic controls of horticultural traits and facilitate marker-assisted breeding in pistachio, we constructed an SSR-based linkage map using an interspecific F-1 population derived from a cross between the cultivar Siirt (Pistacia vera L.) and the monoecious Pa-18 genotype of Pistacia atlantica Desf. This population was also used for the first QTL analysis in pistachio on leaf and shoot characters. In total, 1312 SSR primers were screened, and 388 loci were successfully integrated into parental linkage maps. The Siirt maternal map contained 306 markers, while the Pa-18 paternal map included 285 markers along the 15 linkage groups. The Siirt map spanned 1410.4cM, with an average marker distance of 4.6cM; the Pa-18 map covered 1362.5cM with an average marker distance of 4.8cM. Phenotypic data were collected during the growing seasons of 2015 and 2016 for four traits: leaf length (LL), leaf width (LW), leaf length/leaf width ratio (LWR), number of leaflet pairs (NLL), and young shoot color (YSC). A total of 17 QTLs were identified in the parental maps. Four QTLs for LL and LW were located on LG2 and LG4, while four QTLs for LWR ratio on LG13 and LG14, two QTLs for NLL and two QTLs for YSC were on LG7 and LG9, respectively, with similar positions in both parental maps. The SSR markers, linkage maps, and QTLs reported here will provide a valuable resource for future molecular and genetic studies in pistachio.