To meet the experimental requirements for developing wide-speed range aircraft, research on a supersonic continuous variable Mach number wind tunnel with a Mach number range of 3 to 4.5 was conducted. A scheme of a continuous variable Mach number nozzle was proposed, followed by the design of the supersonic continuous variable Mach number wind tunnel and the calibration of its flow field. Based on P-M (Prandtl-Meyer) expansion theory, a nozzle with single-degree-of-freedom adjustment was designed to achieve continuous variable Mach number. Numerical calculations and calibration experiments were adopted to verify the variable Mach number scheme. Numerical calculation results show that the flow field of the variable Mach number nozzle is uniform at different Mach number. The nozzle centerline Mach number calibration gave the Mach number root mean square, maximum deviation and error. The exit Mach number-expansion angle relation fits P-M theory. The supersonic continuous wave-damping variable Mach number wind tunnel achieves the design goal of continuously changing the Mach number by controlling the nozzle rotation angle while ensuring a high-quality experimental flow field, providing a simplified scheme for experimental research equipment of supersonic variable Mach number flow.