Weed control in broadacre cropping systems is becoming increasingly difficult owing to widespread evolution of herbicide resistance in major weed species. The importance of crop competition in weed management is often overlooked but it can play an important role in cropping systems. Competitive ability of 86 wheat (Triticum aestivum L.) genotypes varying for early vigour was investigated at two sites over two growing seasons against cultivated oats (Avena sativa L.) as a weed mimic. There were significant (P < 0.001) treatment effects of weed, wheat genotype and weed × genotype interaction at the different sites. Mature crop height and early crop vigour were strongly correlated with improved weed suppression and tolerance. Negative correlation between early vigour (normalised difference vegetation index and visual score) and weed-free yield indicates the presence of some yield penalty in high-vigour (HV) lines. Wheat genotypes with high grain yield under weed-free conditions tended to suffer high yield loss from weeds (low tolerance) and allowed greater production of weed seed (low weed suppression). However, many of the HV lines produced significantly higher grain yield than the tested commercial cultivars under weedy conditions. The use of the Finlay–Wilkinson regression approach for assessing cultivar stability revealed a strong association between genotype mean weed suppression and stability across the four environments. Several HV lines showed consistently greater weed suppression than the wheat cultivars investigated. Genotypic variation was much greater for weed suppression than weed tolerance, suggesting greater opportunity for the selection of improved weed suppression in wheat. However, strong positive correlation between weed suppression and tolerance (r = 0.79, P < 0.001) suggests that wheat lines selected on the basis of high weed suppression may also exhibit improved weed tolerance.