In the paper we report on growth conditions, morphology, crystallographic structure and magnetic anisotropy of 20 nm thick, palladium-rich Pd1 - xFex(0.01 < x < 0.1) alloy films grown on (001)-oriented MgO single-crystal substrate. Molecular beam deposition at ultra-high vacuum conditions has been utilized along with the three-step procedure to achieve the epitaxy conditions for the synthesized films. The scanning electron microscopy and atomic force microscopy have shown flat and smooth morphology of the films studied in a wide range of lateral scales. In situ low energy electron diffraction and ex situ X-ray diffraction measurements confirmed that our Pd(1 )(- x)Fe(x )alloy films are epitaxial. Ferromagnetic resonance investigations have shown the in-plane four-fold magnetocrystalline anisotropy characteristic for single-crystalline films with the cubic structure. The whole set of our measurements testifies the epitaxial cube-on-cube growth and excellent magnetic homogeneity of Pd1 - xFex films on MgO substrate obtained within the three-step deposition process.