This paper presents a numerical investigation of the flow characteristics around a freely falling square shape particle in a two-dimensional channel. The FSI (fluid-solid interaction) has been realized by using the direct-forcing/fictitious domain (DF/FD) method. In order to identify the effect of fluid property on the flow characteristics and solid motion by FSI, a wide range of the fluid viscosity has been considered, which introduces various Reynolds numbers to this study. In addition, the off-centered distance of the square particle has been imposed to research the effect of the initial position. The centered particle is freely falling without rotation and transverse motion. However, the motion of the off-centered particle is significantly depended on the Reynolds number, so it is classified into the four regimes by the flow and moving characteristics of the particle. Quantitative information about the drag coefficient on the square particle is highlighted.