A nonstoichiometric ternary antimonide, Zr3.55Pt4Sb4, with a new structure type (hP24), has been synthesized via arc-melting. Its crystal structure was determined by single-crystal X-ray diffraction with hexagonal space group P63/mmc and lattice parameters a = 4.391(3) Å, c = 30.53(2) Å, and V = 509.7(8) Å3. It features the unique Pt4Sb4 slab with Pt-Pt bonds and is reminiscent to hexagonal diamond substructures. Three different Zr atoms, occupying three different sites, aid in the close-packing of the Pt and Sb atoms. Electronic structure calculations show the half occupancy of one Zr site creates a pseudogap at the Fermi level and optimizes the Pt-Sb bonding interactions. This enhances the electronic stability and accounts for the very narrow phase width observed for this nonstoichiometric compound. Furthermore, strong Zr-Pt and Zr-Sb interactions play a crucial role in the chemical bonding of the title compound. Electrical transport measurements show metallic behavior of this compound down to 2 K, consistent with the band structure calculations.