The effect of single‐ion anisotropy is investigated on a mixed‐spin (1, 3/2) square Ising nanowire with square ferromagnetic shell and negative core–shell exchange coupling using Monte Carlo simulation. Depending on the Hamiltonian parameters, three different topologies of the phase diagram in the (anisotropy, temperature) plane are found. The tricritical point appears for and effects. For influence of , there is no tricritical point in the phase diagram. The first‐order lines and critical endpoints are also obtained. Some important phenomena such as compensation behavior and rich variety of hysteresis loops are found. The results can be compared with other works, in particular on the nanowire with core–shell structure.