By using the methods of theoretical analysis and numerical simulation, the relativistic effects of the thermodynamic properties of Fermi gas in a strong magnetic field are studied, and the influential mechanisms of temperatures and the magnetic field on the relativistic effects of the system are analyzed. It is shown that, at low temperatures, the effects of temperatures on the relativistic effect relate to the chemical potential of the free system. The magnetic field's effects on the relativistic effects of heat capacity and chemical potential display oscillating characteristics. At high temperatures, the relativistic effects of the thermodynamic quantities trigger oscillations with increasing of temperatures and magnetic field, and its amplitude decreases obviously to disappearing with the increasing of temperatures. However, its amplitude increases evidently due to the amplified magnetic field.