Recent research suggests that jump squats with a loaded hexagonal barbell are superior for peak power production to comparable loads in a traditional barbell loaded jump squat. The aim of this study was to investigate the relationship between relative peak power output during performance of the hexagonal barbell jump squat (HBJS), countermovement jump (CMJ) height, and linear acceleration speed in rugby union players. Seventeen professional rugby union players performed 10- and 20-m sprints, followed by a set of 3 unloaded CMJs and a set of 3 HBJS at a previously determined optimal load corresponding with peak power output. The relationship between HBJS relative peak power output, 10- and 20-m sprint time, and CMJ height was investigated using correlation analysis. The contribution of HBJS relative peak power output and CMJ height to 10- and 20-m sprint time was investigated using standard multiple regression. Strong, significant, inverse correlations were observed between HBJS relative peak power output, 10-m sprint time (r = -0.70, p < 0.01), and 20-m sprint time (r = -0.75, p < 0.01). A strong, significant, positive correlation was observed between HBJS relative peak power output and CMJ height (r = 0.80, p < 0.01). Together, HBJS relative peak power output and CMJ height explained 46% of the variance in 10-m sprint time while explaining 59% of the variance in 20-m sprint time. The findings of the current study demonstrate a significant relationship between relative peak power in the HBJS and athletic performance as quantified by CMJ height and 10- and 20-m sprint time.