In view of the significance of non-spherical and permeable particles in liquid-solid and gas-liquid-solid reactors in industrial processes, it is essential to understand and quantify the rheological properties of multiphase flows in these processes. In this study, we investigate the shear viscosity of dilute suspension containing elliptical porous particles at low Reynolds number Re of O(0) by use of a modified lattice Boltzmann model. The fluid flow around and inside an elliptical porous particle is described by the volume-averaged macroscopic governing equations. The relative viscosity is calculated for an elliptical porous particle rotating in a two-dimensional (2D) simple shear flow, based on the relation between the shear stress and the second order moments of non-equilibrium particle distribution function. The effects of porous structure of the elliptical particle on the viscosity and flow field are investigated with different axis ratios in detail. Our results demonstrate that the relative viscosities of dilute suspension containing elliptical porous particles increase linearly with solid volume fraction at various Darcy number for particles with varying axis ratios. Moreover, a simple empirical expression for intrinsic viscosity is proposed as a function of Darcy number. (C) 2019 Elsevier B.V. All rights reserved.