Density functional theory (DFT) calculations of the energy of magnetic anisotropy for diluted ferromagnetic semiconductor Ge(1-x)Mn(x)Te were performed using OpenMX package with fully relativistic pseudopotentials. The influence of hole concentration and magnetic ion neighbourhood on magnetic anisotropy energy is presented. Analysis of microscopic mechanism of magnetic anisotropy is provided, in particular the role of spin-orbit coupling, spin polarization and spatial changes of electron density are discussed. The calculations are in accordance with the experimental observation of perpendicular magnetic anisotropy in rhombohedral Ge(1-x)Mn(x)Te (1 1 1) thin layers.