The asymmetric Fano-resonance spectra was proposed to obtain a larger sharpness and elevate the sensitivity of ring resonator, the Eye-like resonator is utilized to generate the asymmetric Fano-resonance spectra, the Eye-like resonator consists two rings resonators with the outer loop coupled to two bus waveguides and the inner loop couple to the outer loop. Numerical calculation of spectra on the drop port was utilized by the transfer matrix method, as the round trip loss varies, the value of sharpness increases with the round trip loss;by changing the outer loop coupling coefficients and inner loop coupling coefficients, the maximum value of sharpness of Fano-resonance change slowly;as the round trip loss varies and a lager range of the outer loop and inner loop coupling coefficients, the corresponding transmission at the resonant point remains almost unchanged, about －6 dB. The sharpness of Fano resonant peak is insensitive for the coupling coefficients, which can reduce the requirements of manufacture of coupling region.