A phase error compensation circuit and a method for compensating a phase error between a reference clock and a feedback clock are provided. The phase error compensation circuit includes a first programmable delay circuit, a second programmable delay circuit and at least one swapping circuit. The first programmable delay circuit provides a first delay. The second programmable delay circuit provides a second delay. At a present cycle, the first delay is unchanged, wherein the swapping circuit applies the first delay to the feedback clock for generating a compensated feedback clock and applies the second delay to the reference clock for generating a compensated reference clock. At a next cycle, the second delay is unchanged, where the swapping circuit applies the second delay to the feedback clock for generating the compensated feedback clock and applies the first delay to the reference clock for generating the compensated reference clock.