Abstract: To understand the self-generated magnetic field induced from the non-parallel property of temperature gradient and density gradient in the ultra-intense laser-plasma interaction, we apply the theoretical analysis and numerical simulation to studying the self-generated magnetic field in consideration of relativistic effects and its generation mechanism, then derive the analytical expressions of self-generated magnetic field, and obtain the time evolution of the spatial distribution of self-generated magnetic field. The simulation results show that once the ultra-intense laser pulse with an intensity of 1019 W/cm2 irradiates the circular concave target, one can observe the self-generated magnetic field with the maximum magnitude at the order of 51102 T on the surface of the plasma, which are consistent with the experimental measurement.