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A ferrimagnetic mixed spin square Blume-Capel Ising nanowire system on spin-1 core and spin-3/2 outer shell have been investigated. The general formula for the temperature dependence of the equilibrium magnetization of the system is presented. The ferrimagnetic core-shell nanosystem shows a compensation point when the exchange interactions are changed for different values of the single-ion anisotropies of shell sublattices and core ones, respectively. So, one can examine interesting phenomena are compensation behaviors and the free energy of the nanosystem, where these phenomena found that the mixed-spin square Blume-Capel Ising nanosystem which is being considered has two compensation temperatures in the range of − 0.8 ≤ D B | J 1 | ≤ − 0.4 , respectively. • We have used mean-field approximation(MFA) for the study of a ferrimagnetic mixed spin square Blume-Capel Ising nanowire system consists of spin-1 core and spin-3/2 outer shell. • Particularly, it has been studied the effect of magnetic anisotropies on an existence of compensation temperature. • Our results predict the possibility of two compensation temperatures depending on the negative values of core, shell crystal fieldsand, respectively. [ABSTRACT FROM AUTHOR]