Wakefield acceleration methods are known due to some their advantages. The main of them is the high accelerating gradient up to several teravolts per meter. In the paper another important advantage is concluded to the possibility of using a wakefield accelerator as a source of electrons by means of obtaining self-injected bunches and their acceleration. The result is the simulation of the process of plasma wakefield excitation by a laser pulse with an energy of tens of mJ and a power of 1…2 TW for obtaining the promising electron source. Homogeneous and Gaussian plasma profiles were investigated and compared to increase the energy of the self-injected bunches. The laser parameters were taken that corresponded to the parameters of the laser setup in the Institute of Plasma Electronics and New Methods of Acceleration of the National Scientific Center “Kharkiv Institute of Physics and Technology”. Based on the results of the simulation, the possibility of obtaining relativistic self-injected bunches that can be used for further laser acceleration experiments, including dielectric laser acceleration, was demonstrated.