The core-degenerate （CD） scenario has been suggested to be a possible progenitor model of type Ia supernovae （SNe Ia）, in which a carbon-oxygen white dwarf merges with the hot CO core of a massive asymptotic giant branch star dur- ing their common-envelope phase. However, the SN Ia birthrates for this scenario are still uncertain. We conducted a detailed investigation into the CD scenario and then gave the birthrates for this scenario using a detailed Monte Carlo binary pop- ulation synthesis approach. We found that the delay times of SNe Ia from this sce- nario are -70 Myr- 1400 Myr, which means that the CD scenario contributes to young SN Ia populations. The Galactic SN Ia birthrates for this scenario are in the range of ~7.4×10^-5 yr^-1- 3.7 × 10^-4 yr^-1, which roughly accounts for -2%-10% of all SNe Ia. This indicates that, under the assumptions made here, the CD scenario only contributes a small portion of all SNe Ia, which is not consistent with the results of Ilkov ＆ Soker.
