Effects of Mach number on the primary breakup of liquid jet in high-speed gas crossflow are numerically investigated. In the applied methodology, the interface movement is directly tracked by a coupled level set and volume of fluid method. The liquid region is solved using an incompressible flow solver, and the gas flow is simulated using a compressible flow solver, with the two solvers coupled at the interface by specifying proper boundary conditions there. The primary breakup processes of liquid jet in both subsonic and supersonic crossflows are simulated at the same Weber number and liquid/gas momentum flux ratio. Different breakup morphologies are numerically predicted at different Mach numbers. The breakup initiation time and the wavelength of surface waves on the liquid column upstream side increase as the Mach number grows. It is observed that gas compressibility results in different pressure distributions around the liquid column at different Mach numbers. The lowest-pressure region at the liquid column periphery makes the liquid column deform faster in subsonic crossflow than in supersonic crossflow. As the Mach number of the crossflow increases, the liquid column penetrates higher in the near-nozzle region while showing a lower spray penetration in the farther-downstream region.