Magnetic properties of free and supported Vanadium clusters of up to four atoms have been calculated self- consistently using the density functional theory. For the free clusters we have used the self- consistent field- linear combination of atomic orbitals- molecular orbital theory with a Gaussian basis for the atom. The geometries, together with the preferred spin multiplicities, were optimized by using the method of steepest descent. For supported clusters on Cu( 001) and Ag( 001), we have used the self- consistent Korringa- Kohn- Rostoker (KKR)- Green"s function approach. Both free and supported clusters are found to be magnetic, although the magnetic moments depend strongly on the cluster size. While free clusters have ferromagnetic ground states, the supported V clusters in general prefer antiferromagnetic configurations. The role of inter- atomic distances, coordination, and surface morphology on the magnetic properties of V clusters are discussed.