The wake behind a particle, namely particle wake, affects the interaction between particle and fluid. This effect of either single or two interactive particles is established for Newtonian fluid flow but not clear for non-Newtonian fluid flow. In this study, The particle wake behaviors and related particle-fluid forces in a power-law fluid flow are studied by a parallel three-dimensional lattice Boltzmann (LB) model over wide ranges of Reynolds number (0.1 < Re < 500) and power-law index (0.6 < n < 1.4). These ranges are well beyond those reported before. A new calibration model is proposed to reduce the discretization effects on the results analysis to most extents. The validity of the LB model with the calibration step is first examined by comparing the calculated fluid drag forces on a single particle against the measurements for different power-law fluid flows. On this basis, the model is used to study the flow and force characteristics resulting from the interaction of non-Newtonian fluid flow with a single particle or two interactive particles with fixed locations. From the simulation data, a new correlation is formulated to predict the drag coefficient of a single particle in power-law fluid flows. Also, the effect of placement distance between two particles is examined. The numerical results reveal the dynamic characteristics of the particle wake and particle-fluid forces, as well as their dependence on the power-law index, Reynolds number, and particles placement. (C) 2017 Elsevier B.V. All rights reserved.