Transmission spectrum of series-coupled micro-ring resonator is analysed with transfer matrix method. It shows that the micro-ring resonator has comb filtering properties. When a pulse train goes through the micro-ring resonator, the frequency of input pulse train is choosed by the comb transmission spectrum of the micro- ring resonator, with the output pulse repetition rate multiplied and the period decreased after inverse Fourier transform. The results demonstrate that the amplitude of output pulse train by a double-ring resonator with equal radius is more uniform and the pulse-repetition rate multiplication (PRRM) effect is much better than by a single-ring resonator with the increase of multiplied pulse-repetition rate. Because series-coupled double-ring resonator with different radii can expand the free spectral range (FSR) and reduce the bending loss of the micro-ring resonator, high frequency and low loss of output pulse train can be obtained when it is used to achieve PRRM. The envelope of output pusle train presents triangle by optimizing the coupling coefficient of the micro-ring resonator, which can greatly improve its practicability.