A method and an apparatus of operating a primary-side-regulation power converter at both continuous current mode and discontinuous current mode are provided. The apparatus includes a switching circuit, a signal generator, a correlation circuit, and a feedback modulator. The signal generator generates a half signal and a second sampling pulse in response to a switching signal. The correlation circuit receives the half signal, the second sampling pulse and a switching-current signal for generating a modulating current. The feedback modulator modulates a feedback signal in response to the modulating current, a detection signal and the switching signal. The detection signal obtained from a transformer is correlated to an output voltage of the primary-side-regulation power converter. An on-period of the half signal is half of an on-period of the switching signal. The switching-current signal is sampled at a falling-edge of the half signal.