As the fundamental physical process with many astrophysical implications, the diffusion of cosmic rays (CRs) is determined by their interaction with magnetohydrodynamic (MHD) turbulence. We consider the magnetic mirroring effect arising from MHD turbulence on the diffusion of CRs. Due to the intrinsic superdiffusion of turbulent magnetic fields, CRs with large pitch angles that undergo mirror reflection, i.e., bouncing CRs, are not trapped between magnetic mirrors, but move diffusively along the magnetic field, leading to a new type of parallel diffusion. This diffusion is in general slower than the diffusion of non-bouncing CRs with small pitch angles that undergo gyroresonant scattering. The critical pitch angle at the balance between magnetic mirroring and pitch-angle scattering is important for determining the diffusion coefficients of both bouncing and non-bouncing CRs and their scalings with the CR energy. We find non-universal energy scalings of diffusion coefficients, depending on the properties of MHD turbulence.1. INTRODUCTION Charged energetic particles or cosmic rays (CRs) are an important ingredient in the physical processes in space and astrophysical environments. It is customary to use the term "energetic particles" in space physics. The theoretical understanding on their acceleration and diffusion in the Solar atmosphere, solar wind, Earth magnetosphere, and heliosphere is important for studying the properties of the interplanetary magnetic field, solar modulation of Galactic CRs, and space weather forecasting (Parker 1965; Jokipii 1971;Singer et al. 2001).The energetic particles with higher energies outside our direct neighborhood, i.e., of Galactic and extragalactic origin, are usually referred to as CRs. The knowledge on the acceleration and diffusion of CRs is essential for probing their sources, explaining their chemical composition, studying their roles in ionizing molecular gas and circumstellar discs (e.g., Schlickeiser et al. 2016;Padovani et al. 2018), driving galactic winds (e.g., Ipavich 1975Holguin et al. 2019), and feedback heating in clusters of galaxies (e.g., Guo & Oh 2008; Brunetti & Jones 2014), as well as modeling the synchrotron foreground emission for cosmic microwave background (CMB) radiation and redshifted 21 cm radiation (e.g., Cho & Lazarian 2002a;Cho et al. 2012). In this work, we focus on the diffusion physics that is generally applicable to energetic particles of Solar origin and CRs. Thus we do not distinguish between them and will only use the term "CRs".