The oxygen mobility in La2-xSrxCuO4-δ (x=0.15; 0.6; 1) was studied by the Molecular Dynamics (MD) technique. The parent layered La2CuO4 crystal structure has been shown to give rise to a strong anisotropy of oxygen diffusion coefficient in the lattice. Equatorial oxygen sites in(CuO2) layers were found to provide the paths of the fast oxygen transport in the structure, while the axial ones in (La2O2) blocks were substantially less mobile. The influence of the dopant concentration on structural properties and energetic characteristics of the oxygen migration are discussed. Analysis of the ion trajectories obtained during the simulation allowed explaining the observed dependence of the oxygen diffusion activation energies on the strontium content and provided further insight into the mechanism of oxygen diffusion in the oxides.