Summary: The lock-up time of a PLL frequency synthesizer mainly depends on the total loop gain. Since the gain of the conventional phase detector is constant, it is difficult to improve the lock-up time by the phase detector. In this paper, we reconsider the operation of the phase detector and propose the PLL frequency synthesizer with multi-phase detector in which the gain of phase detector is increased by using four stage phase detectors and charge pumps. Then, a higher speed lock-up time and good spurious characteristics can be achieved.