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 .