Single crystals of vanadium-molybdenum oxide were grown by chemical-vapor transport method. Two different crystals with almost same chemical formulae were grown there. One is expressed by the formula VOMoO4, and is made of linear chains of VO6 octahedra along the c-axis. The magnetic susceptibility, chi, shows a broad maximum around 100 K, and decreases toward 0 K. This behavior is characteristic in 1D antiferromagnetism. The estimated J(parallel to) and J(perpendicular to) are 82 and 68 K, respectively. At 34 K a sharp transition was observed, which suggests a formation of ferromagnetic order, though the numerical value of chi is too small for a usual ferromagnet. The second crystal is a platelet with a 2D structure. The temperature dependence of chi suggests a formation of ferrimagnetic order at lower temperature. (C) 1998 Elsevier Science B.V. All rights reserved.