The new ternary magnesium rhodium boride Mg2Rh1-xB6+2x has been prepared by the reaction of the mixture of Mg powder, RhB, and crystalline boron in a Ta container sealed under argon. The crystal structure of Mg2Rh0.75(1)B6.50(4) is determined using single-crystal X-ray diffraction, electron diffraction, and high-resolution electron microscopy (space group Pbam, a=8.795(2) A, b=11.060(2) A, c=3.5279(5) A, Z=4, 630 reflections, RF=0.045). It represents a modified Y2ReB6 structure type with an unusual replacement of part of the Rh atoms by boron pairs located in the pentagonal channels parallel to the c axis. The pairs interconnect the neighboring planar boron nets into the 3D framework. The variation of the lattice parameters reveals a homogeneity range Mg2Rh1-xB6+2x. The random distribution of the Rh atoms and boron pairs and the stabilizing effect of the boron pairs on the Y2ReB6 type structure motif are discussed using electronic band structure calculations and chemical bonding analysis with the electron localization function (ELF).