This paper presents the results of the authors’ own research and literature research on the impact of selected environmental and agronomical factors on the yield of potato grown under the organic system and the possibility of increasing the yield. The results are based on research conducted for several years at the Institute of Plant Breeding and Acclimatization in Jadwisin, Poland. The influence of factors such as soil quality and climatic conditions, selection of varieties, seed potato preparation, irrigation of plantations, complementary fertilization, and protection against the late blight was described. The aim of this work was to indicate which of these factors affect the yield increase and to what extent. It was stated that it is possible to increase the yield of potato tubers grown under the organic system through all of the proposed treatments. In our studies, using drip irrigation and complementary fertilization had the greatest effect (25.5% and 19%, respectively). Seed potato presprouting had a smaller influence (4.3%) on the final tuber yield. In the years with high pressure of the pathogen Phytophthora infestans, the selection of cultivars with high resistance was very important. Most of the agronomical treatments not only improved the total yield of tubers, but also increased the share of tubers with a larger diameter. A very high variability of potato yielding depending on weather conditions and a selection of cultivars was emphasized. We can say that a proper agronomical practice carried out on an organic potato plantation can largely eliminate the yielding gap between a conventional and an organic system.