We present the first estimate of the black hole mass function (BHMF) of broad-line quasars (BLQSOs) that self-consistently corrects for incompleteness and the statistical uncertainty in the mass estimates, based on a sample of 9886 quasars at 1 < z < 4.5 drawn from the Sloan Digital Sky Survey. We find evidence for “cosmic downsizing” of black holes in BLQSOs, where the peak in their number density shifts to higher redshift with increasing black hole mass. We estimate the lifetime of the BLQSO phase to be 70 ± 5 Myr for supermassive black holes (SMBHs) at z = 1 with a mass of MBH = 109M⊙, and we constrain the maximum mass of a black hole in a BLQSO to be ~ 1010M⊙. We find that most BLQSOs are not radiating at or near the Eddington limit. Our results are consistent with models for self-regulated black hole growth, where the BLQSO phase occurs at the end of a fueling event when black hole feedback unbinds the accreting gas.