Potato tuber quality is influenced by the interaction of soil nutrients. Hence, simple correlation analysis cannot accurately reflect the true relationship between soil nutrients and potato tuber quality. In this study, potato tuber quality and soil nutrient content were used as research materials in the Loess Plateau of China. The partial least square regression (PLSR) method was used to establish the regression equation between potato quality and soil nutrient. The major soil nutrient indexes influencing potato quality were screened out to provide theoretical basis for potato field management. The results showed that the major soil nutrient factors influencing the potato tuber quality in Loess Plateau were soil ammonium nitrogen, soil nitrate nitrogen, soil available phosphorus, pH, and soil available potassium. Soil pH value is the most important factor affecting potato starch, reducing sugar content, and soluble protein content. Soil nitrate nitrogen is one of the important factors affecting potato tuber soluble total sugar content, vitamin C, browning intensity, and polyphenol oxidase activity. Soil ammonium nitrogen was positively correlated with the total soluble sugar content of potato tubers, and negatively correlated with reducing sugar content, browning intensity, and polyphenol oxidase activity. However, soil available potassium has positive effects on potato starch and reducing sugar content, and negative effects on soluble protein and browning strength. Results of this study indicates that the major soil nutrient factors influencing potato tuber quality were soil nitrate nitrogen and soil pH value.