ILC (International Linear Collider) is a future project of high energy physics. In the current baseline design, positron generation by gamma rays from undulator radiation is assumed. However, this approach is totally new and it is very difficult to demonstrate the system prior to the construction because it requires more than 100 GeV beam as the driver. A conventional positron generation (e-driven) has been proposed as a technical backup option. In this method, the technology is well established, but the issue is to obtain an enough amount of positron with a manageable energy deposition on target. We present a result of a systematic study of capture efficiency defined by DR (Damping Ring) acceptance where the beam emittance is reduced by radiation damping. We performed a start-to-end simulation of the positron source of ILC and found that an enough amount of the positron per bunch is obtained with a manageable energy deposition on the production target.