This paper presents the results of a study that examined the impact of grape variety on the volatile aroma compounds and sensory properties of standard and Muscat grape brandy produced in the Podgorica sub-region (Montenegro) in vintages 2011, 2012, and 2013. The brandies were prepared by the distillation of crushed grapes, from the autochthonous varieties of Vranac and Kratošija, and Muscat grapes, in a traditional copper alembic, under the same conditions. The gas chromatographic-mass spectrometric (GC/MS) method of 82 volatile aroma compounds that belong to the group (alcohols, volatile acids, volatile esters, terpenes, volatile aldehydes, acetals, ethers, ketones, and alkanes) and an evaluation of the sensory properties of brandies were carried out to determine the typical characteristics of the examined brandies. Alcohols, fatty acid esters, and terpene compound contents were significantly more abundant in all Muscat grape brandies compared to the brandies from the Vranac and Kratošija wine varieties (Standard brandy). Research results revealed that variety had a significant impact on the volatile aroma compound and sensory properties of brandy. The varietal effect was also confirmed, by multivariate analysis, based on the aroma volatile composition, which showed a grouping by type of grape brandy (varietal origin). Sensory analyses showed that all the brandies belonged to the category of high-quality brandies.