The structural, electronic, and magnetic properties of cobalt-benzene complexes (Co(n)Bz(m), n, m = 1-4 m = n, n + 1) have been explored within the framework of an all electron gradient-corrected density functional theory. Sandwich conformations are energetically preferred for the smallest series of n, m = 1-2, rice-ball structures are for larger sizes with n >= 3 and both motifs coexist for Co(2)BZ(3). The rice-ball clusters of (3, 3) and (4, 4) are more stable than (3, 4) having a relative large binding energy and HOMO-LUMO gap whereas smaller sandwich clusters have highly kinetic stability at (n, n + 1). The computed ionization potentials and magnetic moments of Co(n)Bz(m) are in good agreement with the measured values overall; the present results suggest that the measured moments are averages reflecting mixtures of a few nearly isoenergetic isomers having different spin states. The magnetism of the complexes mainly comes from Co atoms with a Bz molecule only possessing very small moments. Ferromagnetic ordering is energetically preferred for smaller complexes with n = 1-3 whereas antiferromagnetic ordering is favored for (4, 4). The relatively smaller moments of Co-n clusters in a Bz matrix indicate that Bz molecules play an attenuation role to the magnetism of the complexes.