A ferrimagnetic nanowire consists of the spin-1/2 core and spin-1 outer shell has been studied. The general formula for the temperature dependence of the longitudinal magnetization of the system is given. The ferrimagnetic core-shell nanowire system exhibits two and three compensation points when the temperature of the system is changed at fixed values of the anisotropy of shell sublattice and longitudinal field, respectively. The competition among the exchange coupling between the outer shell and core, the outer shell coupling, the anisotropy, the applied field, and the temperature has a considerable effect on the characteristic of magnetic properties in a two-dimensional nanowire system.