  Recent investigations on the delay time of type Ia supernovae have set useful
constraints on the progenitors of type Ia supernovae. Here we have calculated
the evolution of close binaries consisting of a white dwarf and a main-sequence
or subgiant companion. We assume that, once Roche lobe overflow occurs a small
fraction of the lost mass from the system forms a circumbinary disk, which
extracts the orbital angular momentum from the system through tidal torques.
Our calculations indicate that the existence of circumbinary disk can enhance
the mass transfer rate and cause secular orbital shrinkage. The white dwarf can
grow in mass efficiently to trigger type Ia supernovae even with relatively
low-mass ($\la 2 M_{\odot}$) donor stars. Thus this scenario suggest a new
possible evolutionary channel to those type Ia supernovae with long delay time
$\sim 1-3$ Gyr.
