A method to design a class of asymmetrical-response dual-band bandpass filters (BPFs) is proposed by using a modified Richard's transformation (MRT) with eighth-wavelength (λ/8) transmission lines. Compared to the traditional frequency transformation with symmetrical property, the proposed MRT method realizes asymmetrical property by introducing two design parameters to modulate the frequency transformation curves. An LC circuit can be transformed by a MRT with each shunt lumped capacitor/inductor being equivalently expressed by two sections of series-cascaded λ/8 transmission lines. With this technique, the bandwidths and center frequencies of the two passbands can be individually adjusted. To prove this proposed method, an asymmetrical dual-band BPF with mixed coupling nature is designed and measured in the end.