On the basis of triplet and its properties, a class of triple-mode and triple-band narrow-band bandpass filters is presented and designed by simultaneously exploiting the three resonant modes in a single rectangular cavity: TE101, TE011, and TM110 modes. The input/output ports of the proposed filter are formed by coupling a waveguide feed to a slot on the side wall of a rectangular cavity. These resonant modes are excited by making use of the position and shape of the slots at input/output of the rectangular cavity without any intra-cavity coupling structure. Besides three poles within the desired passband, a pair of transmission zeros (TZs) can be produced and controlled to appear at the inner or outer sides of this passband. Due to emergence of the three resonant modes and realization of a pair of TZs, a highly attenuated and sharpened filtering selectivity is achieved. In order to verify the proposed approach, two filter prototypes are in final fabricated and measured.