  The single-degenerate (SD) model is one of the principal models for the
progenitors of type Ia supernovae (SNe Ia), but some of the predictions in the
most widely studied version of the SD model, i.e. the optically thick wind
(OTW) model, have not been confirmed by observations. Here, we propose a new
version of the SD model in which a common envelope (CE) is assumed to form when
the mass-transfer rate between a carbon-oxygen white dwarf (CO WD) and its
companion exceeds a critical accretion rate. The WD may gradually increase its
mass at the base of the CE. Due to the large nuclear luminosity for stable
hydrogen burning, the CE may expand to giant dimensions and will lose mass from
the surface of the CE by a CE wind (CEW). Because of the low CE density, the
binary system will avoid a fast spiral-in phase and finally re-emerge from the
CE phase. Our model may share the virtues of the OTW model but avoid some of
its shortcomings. We performed binary stellar evolution calculations for more
than 1100 close WD + MS binaries. Compared with the OTW model, the parameter
space for SNe Ia from our CEW model extends to more massive companions and less
massive WDs. Correspondingly, the Galactic birth rate from the CEW model is
higher than that from the OTW model by $\sim$30\%. Finally, we discuss the
uncertainties of the CEW model and the differences between our CEW model and
the OTW model.
