In this letter, new compact third-order single- and dual-band filters on a hexa-modes half-mode substrate integrated waveguide (HMSIW) resonator with loaded H-shaped slot are presented. For the single-band design, the TE101 mode, TE201 mode, and the lower part of H-shaped slot mode are utilized to realize the third-order filtering response. By properly allocating the high-order modes, wide-stopband performance is also obtained. For the dual-band design, the TE101 mode, TE201 mode, and the lower part of H-shaped slot mode are used to realize the third-order lower passband, and the TE202 mode, TE302 mode, and the upper part of H-shaped slot mode are used to realize the third-order upper passband. The operating frequency and bandwidth of the proposed single-/dual-band filters both can be independently controlled. To validate the design concept, two prototypes of third-order single- and dual-band HMSIW bandpass filters (BPFs) are designed, fabricated, and tested. The simulated and measured results agree well with each other.