The response of sweet potato Rainha Branca cv., cultivated under different K2O levels was evaluated. The experiment was carried out in randomized blocks design with four replications in a Quartz psamment soil at Universidade Federal da Paraiba, Paraiba State, Brazil, from July to November/2004. The K2O levels applied were 0; 50; 100; 150; 200 and 250 kg ha-1). The plots consisted of 48 plants, spaced of 0.80x0.30 m. The maximum estimated values, 14.8 and 8.4 t ha-1 of total and commercial roots yield, were obtained with 194 and 174 kg ha-1 of K2O, respectively. However, the most economic level of commercial roots yield (6.0 t ha-1) was reached using 163 kg ha-1 of K2O. The K2O levels resulting in maximum roots yield and economic return, were correlated respectively with 125 and 121 mg dm-3 of available K with Mehlich 1 extractor. The probability for sweet potato response under potassic fertilization in similar soils will be minimized if the level of available K in the soil were superior to 121 mg dm-3. For utilized soil in this study, 163 kg ha-1 of K2O can be recommended for sweet potato fertilization.