We have studied the crystal structure of the AmCm binary alloy under high pressure by means of first-principles self-consistent total-energy calculations using the generalized gradient approximation (GGA) for the density functional theory (DFT). The virtual crystal approximation (VCA) is used for the description of the alloy system. In the present study, we investigated the double hexagonal (P63/mmc) structure, the face centered cubic (Fm3m) structure, the face-centered orthorhombic (Fddd) structure and the primitive orthorhombic (Pnma) structure for the AmCm alloy. Antiferromagnetic calculations have been compared with ferromagnetic calculations for all these phases. Our results are in general good agreement with recent experiment performed by Lindbaum et al. [J. Phys.: Condens. Matter. 15, S2297 (2003)].