Integrating cover crops into vegetable cropping systems can provide a wide range of ecological services, of which weed management is a key component. Cover crop effects on weed control, however, are dependent on termination methods and weed species present in specific cropping seasons. A 2-year weed management experiment with two cultivars of organic zucchini (Cucurbita pepo L.) in central Italy was carried out to compare the effect of a barley (Hordeum distichum L.) cover crop terminated with a modified roller-crimper (RC) to incorporated barley as green manure (GM) and a tilled control left fallow (FA) in the off-season. The effects of cover-crop management on crop competitiveness, yields and weed populations were evaluated by direct measurement, visual estimation and competition index methods. Results showed a significant reduction in weed biomass (>80%) and weed abundance with the RC compared to the GM and FA treatments. Moreover, the RC barley mulch maintained weed control in zucchini plots even under high weed pressure, as determined by the agronomic tolerance to competition (ATC) value of 67% in the RC treatment compared to 40 and 34% in the FA and GM treatments, respectively, averaged over both years of the experiment. The competitive balance (C
b), which quantified the ability of the zucchini crop to compete with weed populations, was also greater (+0.37) in the RC treatment compared to FA (−0.87) and GM (−0.69) treatments over the same period. Zucchini crop biomass was greatest in the RC treatment in 2011. Zucchini fruit yields varied from an average over both years of 1.4 Mg ha−1 in the RC treatment to 0.7 Mg ha−1 in the GM treatment, but yields in the FA treatment, 1.2 Mg ha−1, did not differ from the RC treatment. No differences in yield between ‘Dietary’ and ‘Every’ zucchini, or any significant interactions between cultivar and cover management related to fruit biomass, were observed. Our findings suggested the viability of the modified RC in creating a barley cover-crop mulch to effectively manage weeds and enhance yields in transplanted zucchini.