Particle suspension, which is closely familiar to daily life, often has non-Newtonian properties. Thus, it is important to understand suspension rheology using non-Newtonian fluids, because that may have hidden potential to develop industrial products of high quality. The solvent of suspension for non-Newtonian fluid is sometimes classified into Bingham, dilatant, and pseudoplastic fluids based on its shear rate and shear stress responses. In the previous studies, phenomena that an elliptical particle reached a certain position in a channel flow with gravity using Bingham fluid was reported by Sobhani et al [1]. Tanaka et al [2] reported how the differences of power-law index affected relative viscosity when particles were distributed at equal intervals. However, there are few studies that focus on multiple particles flow using Bingham fluid. Then, we used Herschel-Bulkley model [3] that can express not only power-law fluid but also Bingham fluid, and considered how Bingham fluid affected relative viscosity and compared with Einstein’s viscosity formula [4]. In this study, governing equation was the regularized lattice Boltzmann method, and the method to express a circular rigid particle was virtual flux method. Herschel-Bulkley model was used as a model to express a solvent. Then, we used relative viscosity and the ratio of effective viscosity so as to evaluate differences of a solvent. The results showed that relative viscosity with Bingham fluid was higher as the number of particles increased, which was consistent with the previous study [2]. We confirmed that effective viscosity with Bingham fluid was higher than that with Newtonian fluid, but its trend with increase in concentration was similar with that with pseudoplastic fluid. In the future, we will analyze particle flow when particles are distributed at random positions, considering particle-particle interactions.