The wind tunnel with variable Mach numbers controlled by a single jack is highly desired in the aerospace, automobile and building industry due to its superior controllability and working range. Decreasing the temperature of a test gas is an efficient and economical approach to achieving higher Reynolds numbers that accommodate all working statuses of test subjects, which however, brings new challenges to the wind tunnel design nowadays. This paper proposes a new design concept of a single-jack variable Mach number nozzle based on its particular cryogenic characteristics, as the nozzle is the core structure to achieve variable Mach numbers. The contours of the nozzle under different Reynolds numbers and Mach numbers are modeled and solved by an incomplete elliptic integral, followed by modification with cryogenic characteristics. A 0.3-m cryogenic wind tunnel is utilized as a validation platform for the nozzle design, resulting in designed contours being in line with the measured contours. Moreover, the root means square (RMS) deviations of Mach number 1.3 at the core position are controlled within 0.011 in low and high temperatures, which surpasses the other existing wind tunnels.