In the article, exchange bias in a ferromagnetic film on an antiferromagnetic substrate is studied. These systems are widely used in spintronics devices to fix the state of one of the ferromagnets. The computer simulation method is used for the study. The Ising model and Metropolis algorithm are used. A thin ferromagnetic film on a semi-infinite antiferromagnetic substrate is considered. The layered antiferromagnet model is used for the substrate. The exchange value for the antiferromagnet is lower than for the ferromagnetic film. The Neel temperature for the substrate is lower than the Curie temperature for the ferromagnetic film. For both components of the system, phase transition temperatures are calculated. The exchange bias field is created by exchange interaction at the interface of the film with the substrate. At temperatures above the Neel temperature, the surface layer for the antiferromagnet is not compensated and does not create exchange bias. The dependence of the exchange bias field on the system's temperature is investigated. Exchange bias shifts the hysteresis loop. The position of the hysteresis loop center determines the exchange bias field. As the temperature decreases, the chess magnetization for the antiferromagnetic substrate and the magnetic moment for the boundary spins layer increase. A computer experiment was performed. The dependence of the exchange bias field on temperature near the phase transition point for the antiferromagnet is linear. As the temperature decreases, the exchange bias becomes constant. This transition is associated with maximizing the chess magnetization of the antiferromagnetic substrate. With a decrease in temperature, the width of the hysteresis loop increases. The width of the hysteresis loop decreases linearly with increasing temperature. A comparison is made with the results of real experiments.