A novel modification of the KCoPO4, δ-phase has been prepared by hydrothermal synthesis at 553 K. The compound crystallizes in the orthorhombic system with the unit-cell parameters a = 8.5031(8), b = 10.2830(5), c = 54.170(4) Å. The crystal structure was determined based on synchrotron low-temperature single-crystal X-ray diffraction data obtained from an inversion twin in the space group P212121 and refined to R = 0.077 for 5156 reflections with I > 3σ(I). The δ-KCoPO4 possesses a new structure type which is based on a framework built from sharing vertices Co- and P-centered tetrahedra. The {CoPO4-}∞ construction of tetrahedra may be described as assembled from networks formed by two topologically diverse six-membered rings of tetrahedra stacked together through vertex-bridging contacts along the a axis. The ratio of the (UUUDDD) and (UUDUDD) rings, where (U) and (D) denote the orientation of the tetrahedra in the six-membered rings up and down relative to the plane grids, is equal to 5:1. The (UUDUDD) rings form bands parallel to the [010] direction each surrounded from both sides along the c axis by slabs of five ribbons width having alternative (UUUDDD) topology. Open in the [100] direction channels incorporate K+ ions; this structural feature permits to suppose ion-conductive and/or electrochemical properties of the title compound. The possible mechanism of the δ → γ phase transition is discussed on the basis of the crystal chemical analysis of the KCoPO4 polymorphs. The title compound orders magnetically at TN = 24.8 K.