A structure of double waveguide coupled micro-ring with feedback was designed.The transfer matrix method was employed to derive the formulas of transmittance and phase shift.According to the formula of transmittance,we drew up the asymmetric Fano resonance curves.By analyzing the effects of the transmission coefficients of every coupling zone on transmittance,we know that the transmittance peak is very narrow when t₁=t₂=t₃=0.2.It shows better filtering characteristic than the structure without feedback.And in the condition mentioned above,the loss coefficients of micro-ring and straight waveguide are both sensitive to transmittance.It shows that when either of the loss coefficients changes from 0.8 to 1,the transmittance peak changes from 0 to 1.In addiction,we find that the delaying coefficient of the peak in the vicinity is 29.1,therefore,the structure can also be used as optical delay device.