Background: The aim of this study was to assess the diet of children with Down syndrome (DS) and to identify potential dietary mistakes made by their parents. Materials and methods: The study was conducted among 195 parents of people with DS between November 2020 and March 2021. Data for the study were collected anonymously using the CAWI method. Results: 122 (62.6%) people with DS did not eliminate any nutrient from their diet. By contrast, in the study group, the following numbers of people reported the following dietary restrictions: 51 (26.2%) gluten, 56 (28.7%) lactose, 17 (8.7%) casein, 26 (13.3%) sucrose, 2 (1.0%) histamine, 2 (1.0%) lectins, and 1 (0.5%) dairy. The most frequent response for vegetable and fruit consumption was once a day, with 83 (42.6%) and 87 (44.6%) parents indicating this. The most frequent response for dairy product consumption was every day, with 72 (36.9%) parents indicating this, while 36 (20%) parents stated that their children do not eat dairy products at all. In the study group, the most frequent response for meat consumption was several times a week, this was indicated by 107 (54.9%) parents, while 1 (0.5%) of them said that their children do not eat meat products at all. The most frequent response for fish consumption was 1–2 times a week, this answer was indicated by 101 (51.8%) parents, while 13 (6.7%) said that their children do not eat these products at all. Conclusions: A majority of the subjects with DS are usually fed in a normal way, but nutritional mistakes are made by the parents. Special attention should be paid to prolonging the period of natural feeding.