We theoretically demonstrate the transmittion spectra and dispersion characteristics based on the electromagnetically induced transparency like effect in the nested fiber double-ring resonator with the transfer matrix theory; the system which are connected by three directional couplers consists of two inner rings, one outer ring and one straight waveguide. The simulation results show that the tunable group delay can be realized by changing the coupling coefficients. In the NDRR coupled Mach-Zehnder interferometer system, we obtained fast light and slow light simultaneously. By adjusting appropriate parameters, we can achive flat band group delay curve that has a profound application in optical interferometer, optical buffer, optical filter, optical modulator, dynamic or static optical sensing field.