A promising method of treatment of many malignant tumors is the boron neutron capture therapy (BNCT). It provides a selective destruction of tumor cells by prior accumulation of a stable boron-10 isotope inside them and subsequent irradiation with epithermal neutrons. As a result of absorption of a neutron by boron, a nuclear reaction occurs with the release of energy in a cell containing boron. To measure the "boron" dose, a small-size neutron detector based on a boron-enriched cast polystyrene scintillator was proposed and developed at the BINP. The paper presents the results of changing the boron dose and the dose of gamma radiation in a water phantom and the comparison of these results with the calculated ones. The obtained result is important for irradiation of small laboratory animals with grafted tumors, large domestic animals with spontaneous tumors, and the planned clinical trials of the technique.