Invasive plants may exhibit priority effects and begin growth before native plants. Priority effects may be an important way that invasive species outcompete native plants. We tested priority effects on the invasive grass Smooth Brome Bromus inermis (cool season C₃), the cosmopolitan and invasive Bermuda grass Cynodon dactylon (warm season C₄) and a native grass species, Red Fescue Festuca rubra (cool season C₃), in the greenhouse. We grew each species alone, with a conspecific neighbor (intraspecific competition), concurrently with one of the two other heterospecifics (interspecific competition), and with a priority effect of one species being present 21 days before the heterospecific neighbor (priority effects). We recorded relative growth rates (RGR), as well as above- and belowground dry biomass. We also used a relative interaction index (RII) to determine the competitive abilities of each of these species. Smooth Brome was significantly heavier than Bermuda and Red Fescue, although Bermuda grass had the highest RGR of the three species. All three species showed stronger effects of intraspecific competition than interspecific competition. Most of the effects were competitive relative to plants grown alone. However, none of these three species exhibited priority effects, unlike a previous study. We conclude that increased competitive ability, particularly of Smooth Brome, may be sufficient to exclude native grasses.