We have studied the antiferromagnetic Blume-Emery-Griffiths model with the repulsive biquadratic coupling in an external magnetic field using the lowest approximation of the cluster variation method which is identical to the mean-field approximation. First, we have investigated the thermal variations of the sublattice magnetizations and obtained four different main topological types. Then, we have calculated the phase diagrams and five main different phase diagram topologies are found. Finally, the discussion and comparison of the phase diagrams are made. (c) 2005 Elsevier B.V. All rights reserved.