Recent observations of Type Ia supernovae ( SNe Ia ) suggest that some of the progenitor white dwarfs ( WDs ) had masses up to 2.4– 2.8 ~ { } M _ { \sun } , highly exceeding the Chandrasekhar mass limit . We present a new single degenerate ( SD ) model for SN Ia progenitors , in which the WD mass possibly reaches 2.3– 2.7 ~ { } M _ { \sun } . Three binary evolution processes are incorporated ; optically thick winds from mass-accreting WDs , mass-stripping from the binary companion star by the WD winds , and WDs being supported by differential rotation . The WD mass can increase by accretion up to 2.3 ( 2.7 ) ~ { } M _ { \sun } from the initial value of 1.1 ( 1.2 ) ~ { } M _ { \sun } , being consistent with high luminosity SNe Ia such as SN 2003fg , SN 2006gz , SN 2007if , and SN 2009dc . There are three characteristic mass ranges of exploding WDs . In an extreme massive case , differentially rotating WDs explode as an SN Ia soon after the WD mass exceeds 2.4 ~ { } M _ { \sun } because of a secular instability at T / |W| \sim 0.14 . For a mid mass range of M _ { WD } = 1.5 – 2.4 ~ { } M _ { \sun } , it takes some time ( spinning-down time ) until carbon is ignited to induce an SN Ia explosion after the WD mass has reached maximum , because it needs a loss or redistribution of angular momentum . For a lower mass case of rigidly rotating WDs , M _ { WD } = 1.38 – 1.5 ~ { } M _ { \sun } , the spinning-down time depends on the timescale of angular momentum loss from the WD . The difference in the spinning-down time may produce the “ prompt ” and “ tardy ” components . We also suggest the very bright super-Chandrasekhar mass SNe Ia are born in a low metallicity environment .