A new magnetic oxide, CuMnVO4, was prepared, and its crystal structure was determined by single-crystal X-ray diffraction. The magnetic properties of CuMnVO4 were characterized by magnetic susceptibility and specific heat measurements, and the spin exchange interactions of CuMnVO4 were analyzed on the basis of spin-polarized electronic band structure calculations, CuMnVO4 contains MnO4 chains made up of edge-sharing MnO6 octahedra containing high-spin Mn2+ cations. Our work shows that CuMnVO4 undergoes a three-dimensional antiferromagnetic transition at similar to 20 K. Both the intrachain and nterchain spin exchanges are antiferromagnetic, and the interchain spin exchange is not negligible compared to the intrachain spin exchange.