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• Mixed spin Ising model on a checkerboard square structure was proposed. • The effect of crystal field and exchange coupling were studied. • The phase diagrams of the critical and compensation temperatures were presented. • Double-loop hysteresis behaviors were found. The magnetic properties and phase diagrams of the mixed spin-1 and spin-1/2 Ising model on a checkerboard square structure have been studied using the Monte Carlo simulations based on the Metropolis update protocol. The system consists of four quartets of alternative spin configurations. We found that the compensation temperature evolves for J 1 <0.6 of the spin-1 assembly and J 2 >1.6 of spin-1/2. Regarding the crystal field strength, a threshold value of D > - 0.8 has been observed. We obtain the N -, Q - and P -type compensation behaviors in the system. The phase diagrams exhibit a second-order phase transition to a paramagnetic phase for small values of D ; hence, the system does not show the tricritical point. However, for large negative values of D a first-order phase transition occurs at the threshold value of J 1. The magnetic hysteresis cycles have been obtained for different values of the exchange interaction, temperature, and crystal field. Finally, the system exhibits the superparamagnetic behavior for a fixed value of the temperature and crystal field. [ABSTRACT FROM AUTHOR]