This research investigated the effects of the specific primary (under-fire) air flowrate (m˙air) on the combustion behavior of a 50–50 wt % blend of raw corn straw (CS) and raw pinewood wastes in a fixed-bed reactor. This parameter was varied in the range of 0.079–0.226 kg m−2 s−1, which changed the overall combustion stoichiometry from air-lean (excess air coefficient λ = 0.73) to air-rich (excess air coefficient λ = 1.25) and affected the combustion efficiency and stability as well as the emissions of hazardous pollutants. It was observed that by increasing m˙air, the ignition delay time first increased and then decreased, the average bed temperatures increased, both the average flame propagation rates and the fuel burning rates increased, and the combustion efficiencies also increased. The emissions of CO as well as those of cumulative gas phase nitrogen compounds increased, the latter mostly because of increasing HCN, while those of NO were rather constant. The emissions of HCl decreased but those of other chlorine-containing species increased. The effect of m˙air on the conversion of sulfur to SO2 was minor. By considering all of the aforesaid factors, a mildly overall air-rich (fuel-lean) (λ = 1.04) operating condition can be suggested for corn-straw/pinewood burning fixed-bed grate-fired reactors.