In this study, the dual-transmission properties of a two-cavity structure comprising three asymmetric fiber Bragg gratings (FBGs) are investigated. The periods or Bragg wavelengths of the three FBGs are different from each other, causing their three stopbands to partially overlap and resulting in two overlapped regions. The sizes of these overlapped regions can be controlled by tuning the FBG periods. In addition, only one wavelength can be transmitted from each of the overlapped regions. Thus, dual-transmission is achieved. However, dual transmission will exhibit an ultranarrow bandwidth if a long cavity is considered. Further, the spacing between two wavelengths can be altered by adjusting the FBG periods. The all-fiber structure proposed in this study can be extended to achieve multiple transmissions exhibiting equal or unequal spacings. The proposed structure can be potentially applied in dual- or multi-wavelength fiber lasers.