  We present new evolutionary models for Type Ia supernova (SN Ia) progenitors,
introducing mass-stripping effect on a main-sequence (MS) or slightly evolved
companion star by winds from a mass-accreting white dwarf (WD). The
mass-stripping attenuates the rate of mass transfer from the companion to the
WD. As a result, quite a massive MS companion can avoid forming a common
envelope and increase the WD mass up to the SN Ia explosion. Including the
mass-stripping effect, we follow binary evolutions of various WD + MS systems
and obtain the parameter region in the initial donor mass - orbital period
plane where SNe Ia occur. The newly obtained SN Ia region extends to donor
masses of 6-7 M_\sun, although its extension depends on the efficiency of
mass-stripping effect. The stripped matter would mainly be distributed on the
orbital plane and form very massive circumstellar matter (CSM) around the SN Ia
progenitor. It can explain massive CSM around SNe Ia/IIn(IIa) 2002ic and 2005gj
as well as tenuous CSM around normal SN Ia 2006X. Our new model suggests the
presence of very young (\lesssim 10^8 yr) populations of SNe Ia, being
consistent with recent observational indications of young population SNe Ia.
