Background Czech nutrition recommendations prioritize health aspects without considering affordability. Low socio-economic groups have the highest risk of nutrition-related noncommunicable diseases and cost has been identified as an obstacle to achieve a healthy diet, making the implementation of affordability into dietary guidelines necessary. The aim of this study was to develop a food basket (FB) for a low income Czech family of four that is nutritionally adequate, health-promoting and culturally acceptable at an affordable price. Methods Linear programming optimisation was used to ascertain that the FB covered the recommended nutrient intakes from the Czech Nutrition Society and from the World Health Organization (WHO). Cost of the FB was calculated on the basis of more than 3900 prices of 330 foods. Within a given cost constraint, all FBs were optimized for the highest possible similarity to the reported food group intake according to the most recent Czech National Food Consumption survey, which was used as a proxy for cultural acceptability. Results The optimised FB affordable at a daily food budget for a Czech family on minimum wage (CZK 177, ~ € 6.8) contained 76 foods and had an average relative deviation of 10% per food category from reported intake. The main deviations were: 72% less sweets and confectionery; 66% less salt; 52% less meat; 50% less milk products; 8% less potatoes; and 484% more milk; 69% more oils and fats; 20% more cereals; and 6% more vegetables. Conclusions The optimised FB can help to guide the development of food-based dietary guidelines for low income households in Czech Republic.