We propose a new model for progenitor systems of Type Ia supernovae. The model consists of an accreting white dwarf and a lobe-filling, low-mass red giant. When the mass accretion rate exceeds a certain critical rate, there is no static envelope solution on the white dwarf. For this case, we find a new strong wind solution, which replaces the static envelope solution. Even if the mass-losing star has a deep convective envelope, the strong wind stabilizes the mass transfer until the mass ratio, q, between the mass-losing star and the mass-accreting white dwarf reaches 1.15, i.e., q < 1.15. A part of the transferred matter can be accumulated on the white dwarf at a rate that is limited to M dot cr = 9.0 x 10-7 (MWD/Msolar - 0.50) Msolar yr-1, and the rest is blown off in the wind. The photospheric temperature is kept around T ~ 1 x 105--2 x 105 K during the wind phase. After the wind stops, the temperature quickly increases up to ~1 x 106 K. The white dwarf steadily burns hydrogen and accretes helium, thereby being able to increase its mass up to 1.38 Msolar and explode as a Type Ia supernova. The expected birth rate of this type of supernovae is consistent with the observed rate of Type Ia supernovae. The hot white dwarf may not be observed during the strong wind phase due to self-absorption by the wind itself. The Strong wind stops when the mass transfer rate decreases below M dot cr. Then it can be observed as a supersoft X-ray source.