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In this article, we studied compensation points in a spins system represented by the Hamiltonian of Blume–Capel of spin-3 and spin-7/2 in a square lattice. Free energy and equations of state were obtained using mean field theory via Bogoliubov inequality. The second-order phase transition was studied in a narrow range of temperature values and single ion anisotropies, in addition to the existence of compensation points within this range. We used the mean-field theory approximation to study compensation points through total magnetization and performed a Monte Carlo Simulation (MCS). In this way, we show the existence of compensation points via mean field and MCS.