The aim of the paper was to evaluate the phenolic acid content and antioxidant properties in potato cultivars with coloured flesh and bright flesh. The study material included eight cultivars of edible potato grown in a temperate climate in Poland. Five cultivars were potato tubers with coloured flesh: “Rote Emma”, “Blue Salad”, “Vitelotte”, “Red Emmalie”, and “Blue Congo”; and three were potato tubers with bright flesh: “Bella Rosa”, “Lord”, and “Tajfun”. In all potato samples under study, four phenolic acids were identified: chlorogenic acid, gallic acid, p-coumaric acid, and caffeic acid. The predominant acid was chlorogenic acid, the levels of which ranged from 62.95 mg·100 g−1 FM to 126.77 mg·100 g−1 FM. The total concentration of the identified phenolic acids was diverse and depended on the genotype of the cultivar and the tuber flesh colour, with coloured-fleshed potatoes having higher phenolic acid contents in comparison to bright-fleshed potato cultivars. The average concentration of phenolic acids in the samples was 89.19 mg∙100 g−1 FM, and the average concentrations of the individual phenolic acids identified were as follows: chlorogenic acid (86.19 mg∙100 g−1 FM), gallic acid (1.18 mg∙100 g−1 FM), p-coumaric acid (0.64 mg∙100 g−1 FM), and caffeic acid (1.18 mg∙100 g−1 FM). In addition, three groups of anthocyanins were identified: pelargonidin-3,5-di-O-glucoside, peonidin-3,5-di-O-glucoside, and petunidin-3,5-di-O-glucoside. Anthocyanins were not found in the “Lord” or “Tajfun” varieties characterised by white tuber flesh. The predominant pigment was petunidin-3,5-di-O-glucoside, with an average content of 23.15 mg∙100 g−1 FM, and the highest value was observed in the “Vitelotte” variety (51.27 mg∙100 g−1 FM). The antioxidant activity of the flesh of the potatoes under study was diverse depending on flesh colour. The FRAP (Ferric Reducing Antioxidant Power) assay indicated higher antioxidant activity of coloured-fleshed potato cultivars. The highest concentration was identified in the “Vitelotte” cultivar flesh and was 114% higher than in the “Lord” cultivar. Similar dependencies were found in the case of the DPPH (2,2-diphenyl-1-picrylhydrazyl) assay; however, in this case, the “Vitelotte” cultivar flesh demonstrated nearly 6.4 times higher antioxidant activity than the “Lord” cultivar. Summarizing our own research, we can conclude that potato varieties with coloured flesh are characterised by a higher content of biologically active substances, including phenolic acids, and antioxidant properties compared to potato tubers with bright flesh.