Boron neutron capture therapy (BNCT) is characterized by a selective effect directly on the cells of malignant tumors. The carried out research showed the perspective of the given kind of therapy concerning malignant tumors of the brain. However, the introduction of BNCT into clinical practice is hampered by the lack of a single protocol for the treatment of patients and the difficulty in using nuclear reactors to produce a neutron beam. This problem can be solved by using a compact accelerator as a source of neutrons, with the possibility of installation in a medical institution. Such a neutron accelerator for BNCT was developed at Budker Institute of Nuclear Physics, Novosibirsk. A neutron beam was obtained on this accelerator, which fully complies with the requirements of BNCT, as confirmed by studies on cell cultures and experiments with laboratory animals. The conducted experiments showed the relative safety of the method with the absence of negative effects on cell cultures and living organisms, and also confirmed the effectiveness of BNCT for malignant brain tumors.