Extreme ultraviolet (EUV) light source is an important part of EUV lithography system in semiconductor manufacturing. The EUV light source requires that the 4p⁶4dⁿ-4p⁵4dⁿ⁺¹ + 4d^n–14f transitions of Sn^8+~13+ ions emit thousands of lines which form unresolved transition arrays near 13.5 nm. Laser-induced discharge plasma is one of the important technical means to excite target into an appropriate plasma condition. Laser-induced discharge plasma has a simple structure and a low cost. It also has important applications in mask inspection, microscopic imaging, and spectral metrology. In the design and production process, there are many factors that can influence the conversion efficiency, such as current, electrode shape, and laser power density. The simulation method is a convenient way to provide guidance for optimizing the parameters. In this paper, a completed radiation magneto-hydrodynamic model is used to explore the dynamic characteristics of laser-induced discharge plasma and its EUV radiation characteristics. To improve the accuracy, a more detailed global equation of state model, an atomic structure calculation model including relativistic effect and a collision radiation model are proposed simultaneously. The simulation reconstructs the discharge process effectively, which is divided into five stages in the first half cycle of current, including expansion of laser plasma, column formation of discharge plasma, diffusion of discharge plasma, contraction of discharge plasma, and re-diffusion of discharge plasma. It is revealed that the pinch effect during the current rising time exerts a significant influence on the generation of EUV radiation. The conversion efficiency of EUV radiation is still low under our existing conditions, and hopefully a higher rising rate of current can improve the conversion efficiency in the future work.