We numerically study the diffusion and scattering of cosmic rays (CRs) together with their acceleration processes in the framework of the modern understanding of magnetohydrodynamic (MHD) turbulence. Based on the properties of compressible MHD turbulence obtained from observations and numerical experiments, we investigate the interaction of CRs with plasma modes. We find that (1) the gyroradius of particles exponentially increases with the acceleration timescale; (2) the momentum diffusion presents the power-law relationship with the gyroradius in the strong turbulence regime, and shows a plateau in the weak turbulence regime implying a stochastic acceleration process; (3) the spatial diffusion is dominated by the parallel diffusion in the sub-Alfv\'enic regime, while it is dominated by the perpendicular diffusion in the super-Alfv\'enic one; (4) as for the interaction of CRs with plasma modes, the particle acceleration is dominated by the fast mode in the high $\beta$ case, while in the low $\beta$ case, it is dominated by the fast and slow modes; (5) in the presence of acceleration, magnetosonic modes still play a critical role in diffusion and scattering processes of CRs, which is in good agreement with the earlier theoretical predictions.
