We present a high-quality, bias-free quantum random number generator (QRNG) using photon arrival time selectively in accordance with the number of photon detection events within a sampling time interval in attenuated light. It is well showed in both theoretical analysis and experiments verification that this random number production method eliminates both bias and correlation perfectly without more post processing and the random number can clearly pass the standard randomness tests. We fulfill theoretical analysis and experimental verification of the method whose rate can reach up to 45Mbps.