Extended main-sequence turnoffs (eMSTO) have been observed in the color-magnitude diagram (CMD) of intermediate-age and young star clusters. The origin of the eMSTO phenomenon is still highly debated. Calculations show that the blue and faint (BF) stars in the CMD of NGC 1866 are hydrogen main sequence (MS) + naked He star systems. The He star derives from the massive star of a binary system. The BF stars and the red and faint MSTO stars belong to the same stellar population. The values of $m_{F336W}$ and $m_{F336W}-m_{F814W}$ of the BF stars are mainly determined by the masses of He stars and H-MS stars, respectively. The behaviors of the BF stars in the CMD are well explained by the H-MS + He-star systems. The BF stars provide a strict restriction on the age of the stellar population. Moreover, the bimodal MS of NGC 1866 can also be reproduced by a younger binary population. The calculations show that part of the blue and bright (BB) MS stars of NGC 1866 are H-MS + He-star systems, H-MS + white dwarf systems, and merged stars in a binary scenario. The H-MS stars of the H-MS + He-star systems for the BB stars are significantly more massive than those of the BF stars. Once the H-MS + He-star systems and their membership in NGC 1866 are confirmed, the extended star-formation histories and the effects of binaries can be confirmed in the young star cluster.
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