A culture pot experiment with sweet potato was conducted to investigate the influence of nitrogen (N) variation on fibrous root growth and storage root differentiation under two levels of soil moisture. Sweet potato plants were supplied with low N (N0, no supplemental N), medium N (N75, 75 mg kg−1), or high N (N150, 150 mg kg−1) under normal water supply (field capacity 75%) or drought (field capacity 50%) conditions. The results indicated that during storage root formation, sweet potato root biomass and storage root differentiation were greater in N75. But high N application inhibited storage root differentiation, root biomass, and morphological traits decreased sharply under drought conditions. Under normal water supply, medium N application promoted a uniform distribution of roots in the 0–30-cm soil layer, whereas excessive N application resulted in roots being distributed mainly on the surface of the soil. Water stress increased deep root growth under the N0, significantly decreased deep root growth under the N150. Under drought stress, the N75 improved the plasticity of the root system and increased Fv/Fm, qP, ETR, and PIABS, which alleviated the effect of drought stress on root growth and maintained the functioning of photosystem II. However, high N affected the pH and EC in the soil layer and was not conducive to root development. All of these results indicate an association between variation in N application and the architectural attributes of sweet potato root. This information has great importance for complete N evaluation to improve root plasticity and drought resistance in sweet potato.