The paper considers the application of a Generative Adversarial Network (GAN) for the development of a generator of deep inelastic lepton-proton scattering. The difficulty of effective training of the generator based on GAN is noted. It is associated with the use of complex schemes of distributions of physical properties (energies, momentum components, etc.) of particles in the process of deeply inelastic lepton-proton scattering. It is shown that the GAN makes it possible to faithfully reproduce the distributions of lepton physical properties in the final state at different initial energies of the center of mass in the range between 20 and 100 GeV.