There is an increasing interest in the use of cover crops in agriculture, in Sweden mainly for the use as catch crops to reduce nitrogen leakage. Some of these crops are known for their allelopathic abilities, which may play a role in the control of weeds and contribute to reduced herbicide use. This study aimed to explore the possible suppressive effect of the cover crop species white mustard, fodder radish, rye, and annual ryegrass on the early growth of the weed species silky windgrass, shepherd's-purse, and scentless false mayweed. In a greenhouse experiment using fresh cover crop residues, white mustard was the only crop that showed an effect. It reduced both seedling establishment, by 51 to 73%, and biomass, by 59 to 86%, of shepherd's-purse and scentless false mayweed. In contrast, in a growth chamber experiment using frozen material, mean germination time of silky windgrass was extended by 20 to 66% by all cover crops. Also, three out of four cover crops reduced root growth in scentless false mayweed by 40 to 46%, and two out of four cover crops reduced root growth in shepherd's-purse by 13 to 61%. However, considering seedling survival, white mustard was the most prominent cover crop, reducing survival by 21 to 57% in shepherd's-purse and scentless false mayweed. In this paper we provide evidence that different weed species show different response to different cover crops under climatic conditions prevailing in Scandinavia. Such results emphasize the importance of understanding weed–cover crop interactions as necessary for developing cropping systems that can utilize cover crops to suppress local weed flora.