By introducing the equivalent four-port network, the general formulas for the series-coupled multiple-ring resonator were derived with the transfer matrix method. The characteristic parameters of series-coupled double-rings resonator such as, amplitude flatness, bandwidth and phase group delay, were analyzed and optimized. Numerical results demonstrated that the propagation loss on the device was negligible with improved fabrication techniques. Since filter performances were determined by the coupling coefficients, the maximal flat response with sharper rolloff could be achieved by setting coupling coefficients symmetric and smaller in the middle. Compared with single-ring resonator, the series-coupled multiple-rings structure obviously improved the amplitude response and eliminated the second-order group delay dispersion.