Owing to the complexity of turbulent magnetic fields, modelling the diffusion of cosmic rays is challenging. Based on the current understanding of anisotropic magnetohydrodynamic (MHD) turbulence, we use test particles to examine the cosmic rays' superdiffusion in the direction perpendicular to the mean magnetic field. By changing Alfven Mach number M-A and sonic Mach number M-S of compressible MHD simulations, our study covers a wide range of astrophysical conditions including subsonic warm gas phase and supersonic cold molecular gas. We show that freely streaming cosmic rays' perpendicular displacement increases as 3/2 to the power of the time travelled along local magnetic field lines. This power-law index changes to 3/4 if the parallel propagation is diffusive. We find that the cosmic rays' parallel mean free path decreases in a power-law relation of M-A(-2) in supersonic turbulence. We investigate the energy fraction of slow, fast, and Alfvenic modes and confirm the dominance of Alfvenic modes in the perpendicular superdiffusion. In particular, the energy fraction of fast mode, which is the main agent for pitch-angle scattering, increases with M-A, but is insensitive to M-S >= 2. Accordingly, our results suggest that the suppressed diffusion in supersonic molecular clouds arises primarily due to the variations of M-A instead of M-S.