  Owing to the complexity of turbulent magnetic fields, modeling 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 traveled 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 $M_S \ge 2$.
Accordingly, our results suggest that the suppressed diffusion in supersonic
molecular clouds arises primarily due to the variations of $M_A$ instead of
$M_S$.
