Weed-competitive rice cultivars, a viable tool for integrated weed management of rice-field weeds, may greatly reduce the weed pressure and excessive dependence on herbicide in controlling weeds. Based on this premise, field experiments were conducted in 2018 and 2019 during the monsoon and winter rice-growing seasons at the Agronomy Field Laboratory of Bangladesh Agricultural University, Bangladesh, to evaluate the weed competitiveness of the selected rice varieties. A total of 42 monsoon and 28 winter rice varieties from Bangladesh were evaluated under “weedy” and “weed-free” conditions in the puddled transplanted system of cultivation. The field experiments were designed with three replications in a randomized complete block design. The results revealed that weed competition greatly reduces the yield of rice, and relative yield loss was 15–68% and 20–50% in monsoon and winter season rice, respectively. The lowest relative yield losses were recorded in monsoon rice from the variety BU dhan 1 (18%) and from the winter rice BRRI hybrid dhan5 (23.7%), which exhibited high weed tolerance. The weed competitive index (WCI) greatly varied among the varieties in both seasons and the monsoon season, ranging from 0.4 to 2.8, and the highest value was recorded from the hybrid variety Dhani Gold followed by BU dhan 1. In winter season rice, the WCI varied 0.25 to 2.4 and the highest value was recorded from the variety BRRI hybrid dhan3, followed by hybrid variety Heera 6. In monsoon rice, hybrid Dhani Gold was the most productive, but BU dhan 1 was the most weed competitive variety. Among the winter-grown varieties, the hybrid Heera 6 was the most productive, and the most weed competitive. Our research confirmed a high degree of variability in weed competitiveness among the 70 Bangladeshi rice varieties tested.