In this work, Monte Carlo simulations based on metropolis algorithm were performed to study the critical and compensation temperatures of a core-shell nanowire with spins [Formula: see text] and [Formula: see text], respectively, considering an Ising antiferromagnetic system. The influence of nearest neighbors exchange interactions and crystal field anisotropy on the critical and compensation behaviors of the system has been analyzed. The effects of the nanowire height in the critical and compensation temperatures were evaluated. The results show that, for a system with given values of exchange interaction constants and crystal field anisotropy, a compensation point only appears if two requirements are satisfied. First, the weight of the core magnetization in the total magnetization must be greater than the weight of the shell magnetization at zero temperature. And second, the exchange constant of shell ions must be greater than a certain value. This value is, at the same time, greater than the exchange constant of core ions. The critical and compensation temperatures are very sensitive to variations in the exchange constant of the shell ions and core ions, respectively, while the crystal field anisotropy affects both temperatures.