Pálinka is a traditional fruit spirit and a kind of gastronomic heritage in Hungary. In Pálinka production, fermentation is one of the most important processes affecting the quality and yield of spirits. Based on single-factor and three-factor influence level tests by following the Plackett–Burman design, the fermentation process from sour cherry juice concentrate and Saccharomyces cerevisiae by using Response Surface Methodology (RSM) coupled with the central composite rotatable design was investigated to optimize fermentation conditions through three variables in a defined range of temperature (1525 °C), pH (2.753.75), and total soluble solid (1830 °Brix). After eight fermentation days, production yields of alcohol and volatile compounds were a maximum of 9.02% v/v and 337.37 mg/L at an optimized temperature of 24.71 °C, pH of 3.25, and total soluble solid of 22.49 Brix. The GC-FID analysis results showed 1-propanol, 2-methyl-1-propanol, 2-methyl-1-butanol, 3-methyl-1-butanol, and ethyl acetate were considered the major aroma compound in the cherry spirits. These results provided important information in serving the basic to develop standard fruit spirits production from sour cherry.