Development of an inelastic zone ahead of a crack tip known as process zone is a common phenomenon observed in many quasi-brittle materials. Some experimental and numerical efforts have been conducted to scrutinize the parameters affecting the size of process zone. This study investigates the role of grain size on the process zone and size effect parameters by conducting a discrete element simulation of rock fracture. A softening contact bond model is used to study the development of the process zone around a notch tip in three-point bending tests. The numerical simulation is utilized to obtain nominal tensile strength, apparent fracture toughness and width of process zone. Bazant's size effect law parameters were obtained using the change in nominal tensile strength with specimen size and it was found that by increasing the grain size, brittleness of the material decreases. It is also shown that apparent fracture toughness is in general a function of specimen and grain size and it increases with the increase in grain size. The change in process zone width with specimen size is investigated too. It is illustrated that for a less brittle material, the impact of grain size on the width of process zone is greater. Based on dimensional analysis, for sufficiently large specimens, a linear relationship between width of process zone and grain size is suggested.