Industrial CFB risers usually handle polydisperse mixtures with broad size distribution, which significantly influenced the performance of the reactors. However, traditional Computational Fluid Dynamics (CFD) models usually assumed that the particle followed the mono-disperse distribution. In the present work, the method of computational particle fluid dynamic (CPFD) was applied for simulating the complex hydrodynamics in the CFB riser with various particle size distributions (PSDs). Two kinds of PSDs, namely Gaussian and Lognormal distribution with various PSD widths, were implemented into the CPFD scheme. With the CPFD method, the present work extensively studied the effects of PSD on the hydrodynamics and on the solids back-mixing. The CPFD results showed that the PSD significantly affected particle's flow behaviors at the lower zone of the riser, while the PSD effects were negligible in the upper part of the riser. This is meaningful for the industrial riser reactors since most of the reaction and transport process occur in this lower zone of the riser. Besides, the simulation results showed that wider PSD dramatically weaken the particle's back-mixing behaviors in the riser. The significant effects of PSD predicted by the CPFD method imply that large errors will be introduced if the mono-disperse assumption is adopted to simulate the experimental CFB riser handling particles with broad size distribution. (C) 2014 Elsevier B.V. All rights reserved.