Active flow control methods based on dielectric barrier discharge plasma actuators can be used to increase the efficiency of combustion systems. In this study, the influence of the location of plasma actuators on the bluff body in a non-premixed burner on the non-reactive flow field of fuel and oxidizer is investigated numerically. Flow field properties and spatial mixing deficiency (SMD) are calculated to evaluate the plasma actuator's influence on the reactants' mixing inside the burner. The results show that the plasma actuator can influence the recirculation areas and are effective in mixing fuel and oxidizer. The presence of the plasma actuator results in the formation of a vortex, which slows down the movement of the flow and improves the mixing between the fuel and airflow streams resulting in more favorable combustion. The results show that at a higher air velocity (4 m/s), the formation of a plasma zone near the air duct strengthens the external circulation zone (ERZ) in such a way that it surrounds the internal recirculation zone and reduces the value of SMD by an average of 7.89%. While activating the actuator also strengthens the ERZ for a lower air velocity (0.3 m/s), this affects the air inflow, and the flow field becomes dominated by the fuel jet flow. When the diameter of the bluff body is increased, both when the plasma actuator is active or inactive, the ERZ is greatly strengthened, and the flow field is more dominated by the airflow.