Abstract: A four factors five levers quadratic general rotary design was used to optimize the planting density and NPK application rates for high yield and high quality sweet potato,"Yanshu 5".A mathematic model was established:Y=53.76143+2.37583X1+3.04500X2+1.38583X3+1.89750X4-1.48932X12-1.07557X22-2.11557X32-2.45807X42+1.56750X1X2+0.29375X1X3+0.69875X1X4+0.71625X2X3+0.35125X2X4+0.23500X3X4.Impact of various factors on the yield of Yanshu 5 was in the order of K P density N.The optimized conditions to achieve a tuber yield of 48-53 thm-2 included: planting density at 57 900-62 600 hm-2 and applications of 46% urea at 321.75-401.4 kghm-2,12% super-phosphate at 400.5-483.9 kghm-2 and 50% potassium at 325.05-388.2 kghm-2.