  Observations have shown that the effective temperature of hydrogen-free
Wolf-Rayet (WR) stars is considerably lower than that of the standard model,
which means that the radius of the observed H-free WR stars is several times
larger than that estimated by the standard model. The envelope inflation
structure (EIS) caused by the radiation luminosity being close to the Eddington
luminosity in the iron opacity peak region of H-free WR stars may be the key to
resolve the radius problem of H-free WR stars. We try to explain the H-free WR
stars observed in the Milk Way (MW) and the Large Magellanic Cloud (LMC) by the
He stars. Using the Modules for Experiments in Stellar Astrophysics code, we
compute the evolution of He stars with and without MLT++ prescriptions and
discuss their effects on the EIS. We have calculated the evolution of He stars
using a new mass-loss rate formula and three different relative rotational
velocity and compared our results with observations on Hertzsprung-Russell
diagrams. The low luminosity (log$(L/L_{{\odot}})\leq5.2$) H-free WR stars in
the MW and the LMC can be explained by the helium giant phase in low-mass He
stars, the high $X_{C}$ and $X_{O}$ in WC stars can only evolve through
low-mass He stars with a rapid rotation. High-mass He stars with the EIS can
explain H-free WR stars with a luminosity exceeding $10^{5.7} L_{{\odot}}$ and
an effective temperature above $10^{4.7}$ K in the MW. They can also explain
H-free WR stars on the right-hand side of the He zero-age main sequence in the
LMC. High-mass stars with the EIS evolve into WO stars at the final evolution
stage, and the shorter lifetime fraction is consistent with the small number of
observed WO stars.
