Field trials were conducted to study response of potato (Solanum tuberosum L) yield and quality to potassium (K) application, soil indigenous K supply (IKS) and productivity (IKP), K use efficiency and critical level of soil test K to establish scientific methods for K management in potato production. Results indicated that K application increased tuber yield by a range of −2.8 to 7.2Mgha−1 with an average of 3.2Mgha−1, 90% positive responses. Potassium application produced an average of 4.9 percentage more commercial rate, 11.3g more mean tuber weight and 0.4 percentage more tuber starch content and 0.2 percentage less tuber sugar content than those of treatment without K application. The average agronomic efficiency of potassium (AEK) was 30.2kg tuber kg−1K2O, 56% observations was in 10–40kg tuber kg−1K2O. 79.2% of the observations showed negative K balance in potato fields with an average of 101.7kgKha−1 deficit. 87.5% of all the observations showed positive benefit from K application with an average return of US$715ha−1. The average IKS and IKP was 141.8kgKha−1 and 25.9Mgha−1 which can be explained 25% and 30% of variations, respectively, by soil exchangeable K. Significant negative quadratic relationship (R2=0.75, P<0.01) between yield response and relative yield, and significant linear relationship (R2=0.80, P<0.01) between yield response and AEK were obtained. There was a significant relationship (R2=0.74, P<0.01) between total uptake K by potato plant and total tuber yield. The critical level of soil exchangeable K at 90% relative yield was 105mgkg−1 which can be a reference for K recommendation.