Existing data-driven approaches for exploring high-entropy alloys (HEAs) face three challenges: numerous element-combination candidates, designing appropriate descriptors, and limited and biased existing data. To overcome these issues, here we show the development of an evidence-based material recommender system (ERS) that adopts Dempster–Shafer theory, a general framework for reasoning with uncertainty. Herein, without using material descriptors, we model, collect and combine pieces of evidence from data about the HEA phase existence of alloys. To evaluate the ERS, we compared its HEA-recommendation capability with those of matrix-factorization- and supervised-learning-based recommender systems on four widely known datasets of up-to-five-component alloys. The k-fold cross-validation on the datasets suggests that the ERS outperforms all competitors. Furthermore, the ERS shows good extrapolation capabilities in recommending quaternary and quinary HEAs. We experimentally validated the most strongly recommended Fe–Co-based magnetic HEA (namely, FeCoMnNi) and confirmed that its thin film shows a body-centered cubic structure.