Palmer amaranth (PA) is one of the major weeds in sweetpotato reducing its quantity and quality. The widespread and repeated use of chemical herbicides has led PA to develop resistance for such chemicals. In addition, chemical herbicides are incompatible with the organic production system. It is imperative to find sustainable weed management strategies to provide weed control suitable for organic cultivation and detain the development of herbicide-resistant weeds under conventional crop production. In the present study, seventeen sweetpotato varieties were screened for their allelopathic (weed-suppressing) effect on the growth of PA. The experiment was conducted in a greenhouse using a stair-step system. Each plant in the stair-step system had its height (cm), chlorophyll concentration (cci) and shoot biomass (g) measured. The variation in the height, chlorophyll and shoot biomass reduction of PA was significant after the third week of transplanting. Three weeks after transplanting (WAT), only three varieties, i.e., Morado (75%), Bayou belle (62%), and Vardaman (61%), reduced PA’s height by >60% compared to the control. While 5 WAT, four varieties, i.e., 529 (93%), Morado (93%), Heartogold (85%), and Centennial (81%), reduced PA height by >80%. Hatteras, Centennial, and 529 reduced the chlorophyll content of PA by >50%. In the presence of Beauregard, the commercial cultivar, there was no reduction in shoot biomass of PA. Cluster analysis also demonstrated that the four allelopathic sweetpotato varieties, i.e., Heart-O-Gold, Centennial, 529, and Morado, were clustered together, indicating that these varieties have similar potential to suppress the growth and development of PA. Combining allelopathic sweetpotato cultivars (Heart-O-Gold, Centennial, 529, and Morado) with other sustainable weed control measures, such as cover crops and hand-weeding, can improve the weed management, espicially in organic farming. However, field experiments should be conducted to confirm the allelopathic as well as yield potential of these varieties in an agronomic setting. The availability of the allelopathic sweetpotato cultivars will benefit organic producers by enhancing crop productivity and decrease reliance on chemical herbicides in conventional farming systems.