Quantum chemical (U)PBE0 method is used to investigate the endometallofullerenes Gd@C70, Gd@C82, Gd@C84, and Gd@C90 for different spin states. The equilibrium structural parameters, IR spectra, the chemical bond energies, the electron affinity and vertical ionization potentials are calculated. The analysis of the electron and spin populations of the atomic orbitals in gadolinium endocomplexes was carried out. For all considered configurations, the calculations predict the polarizability depression and a high value of the magnetic moment. The endocomplex has the same high value of multi-electron spin as the free gadolinium atom, that characterizes its significant magnetic properties.