The machine learning (ML) models were proposed for predicting elastic properties of face-centered-cubic (FCC) high-entropy alloys (HEAs). The data set was from the first-principles calculation, which contained 186 samples. The goodness-of-fit (R²) values of predicted bulk modulus (B) and shear modulus (G) in the test set were 0.81 and 0.84, respectively. According to the results of ML, CoNiCuMoW HEAs have the largest B, G, elastic modulus (Y) and good ductility (G/B≤0.57) among the FCC HEAs with equal components. The first-principles calculation results show that the elastic anisotropy of (CoNiCuMo)_1-xW_x HEAs increases and ductility decreases with increasing W content. According to the analysis of charge density difference, there is obvious charge accumulation at W—W and W—Mo bonds, indicating the directional covalent bonds formed between W atoms and their neighboring atoms.