Some Type Ia supernovae (SNe Ia) are suggested to have progenitor white dwarfs (WDs) with mass of up to 2.4-2.8 M⊙, highly exceeding the Chandrasekhar mass limit. We present a new single degenerate (SD) model for SNe Ia progenitors, in which the WD mass can increase by accretion up to 2.3 (2.7) M⊙ from the initial value of 1.1 (1.2) M⊙. The results are 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 a SNe Ia soon after the WD mass exceeds 2.4 M⊙ because of a secular instability at T/|W|~0.14. For a mid mass range of MWD = 1.5-2.4 M⊙, which is supported by differential rotation, it takes some spinning-down time until carbon is ignited to induce an SN Ia explosion. For a lower mass range of MWD = 1.38-1.5 M ⊙, they can be supported by rigid rotation until the angular momentum is lost. We also suggest the ultra super-Chandrasekhar mass SNe Ia are born in young and low metallicity environments.