  A newly developed 3-D Monte Carlo model is used, in conjunction with a
multi-line non-LTE radiative transfer model, to determine the mass-loss rate of
the Wolf-Rayet (W-R) star in the massive binary \object{V444 Cyg} (WN5+O6).
This independent estimate of mass-loss rate is attained by fitting the observed
\HeI (5876) \AA and \HeII (5412) \AA line profiles, and the continuum light
curves of three Stokes parameters ((I, Q, U)) in the (V) band simultaneously.
The high accuracy of our determination arises from the use of many
observational constraints, and the sensitivity of the continuum polarization to
the mass-loss rate. Our best fit model suggests that the mass-loss rate of the
system is (\dot{M}_{\WR}=0.6(\pm 0.2) \times 10^{-5} M_{\sun} \mathrm{yr}^{-1}
), and is independent of the assumed distance to \object{V444 Cyg}. The fits
did not allow a unique value for the radius of the W-R star to be derived. The
range of the volume filling factor for the W-R star atmosphere is estimated to
be in the range of 0.050 (for $R_{\WR}=5.0 R_{\sun}$) to 0.075 (for
$R_{\WR}=2.5 R_{\sun}$). We also found that the blue-side of \HeI (5876 ) \AA
and \HeII (5412) \AA lines at phase 0.8 is relatively unaffected by the
emission from the wind-wind interaction zone and the absorption by the O-star
atmosphere; hence, the profiles at this phase are suitable for spectral line
fittings using a spherical radiative transfer model.
