  Recent discovery of several overluminous type Ia supernovae (SNe Ia)
indicates that the explosive masses of white dwarfs may significantly exceed
the canonical Chandrasekhar mass limit. Rapid differential rotation may support
these massive white dwarfs. Based on the single-degenerate scenario, and
assuming that the white dwarfs would differentially rotate when the accretion
rate $\dot{M}>3\times 10^{-7}M_{\odot}\rm yr^{-1}$, employing Eggleton's
stellar evolution code we have performed the numerical calculations for $\sim$
1000 binary systems consisting of a He star and a CO white dwarf (WD). We
present the initial parameters in the orbital period - helium star mass plane
(for WD masses of $1.0 M_{\odot}$ and $1.2 M_{\odot}$, respectively), which
lead to super-Chandrasekhar mass SNe Ia. Our results indicate that, for an
initial massive WD of $1.2 M_{\odot}$, a large number of SNe Ia may result from
super-Chandrasekhar mass WDs, and the highest mass of the WD at the moment of
SNe Ia explosion is 1.81 $M_\odot$, but very massive ($>1.85M_{\odot}$) WDs
cannot be formed. However, when the initial mass of WDs is $1.0 M_{\odot}$, the
explosive masses of SNe Ia are nearly uniform, which is consistent with the
rareness of super-Chandrasekhar mass SNe Ia in observations.
