Abstract Using the stellar evolution code—Modules for Experiments in Stellar Astrophysics (MESA)—we investigate the evolution of massive stars with different rotational velocities and metallicities towards Wolf-Rayet stars. In our simulations, the initial rotating velocities are taken as 0, 250, 500, and 650 km s?1, and the metallicities equal to 0.02, 0.014, 0.008, 0.006, 0.004, and 0.002. We show our rapid rotation models in the HR diagram compared with the observations. We find that the rotational mixing is less efficient at high metallicity, and these stars become Wolf-Rayet (WR) stars when the helium in their center is ignited. However, rapid rotating massive stars at low metallicity can easily evolve into WR stars due to the rotation resulted in chemically homogeneous evolution. This can explain the origin of single WR stars in galaxy at low metallicity. In our models, the observed SMC WR stars are consistent with the single-star evolution models. However, at higher metallicities our single-star evolution models can only explain the luminous, hydrogen-rich WN stars and O stars (which are classified as WR stars previously).