Modeling analysis of underwater pulsed arc discharge can predict the characteristics of plasma channels, providing theoretical guidance for the practical application of underwater pulsed discharge. Due to the complexity of experimental diagnostics for ‘kA’-level underwater pulsed discharge, there is currently a lack of precise experimental data to support the initial value selection and result optimization of the modeling. This paper established a plasma channel model for underwater pulsed arc discharge. In conjunction with the Saha ionization equilibrium equation, the model was capable of simulating the current, pressure, temperature, and electron density of the channel after gap breakdown. By utilizing spectroscopic diagnostic data and a multi-objective optimization algorithm, the initial values and key parameters of the model were reasonably determined. The simulation results were in good agreement with the experimental diagnostic results, reasonably representing the trends in electron density and blackbody radiation temperature. Moreover, the model was applicable for reasonably explaining the emission spectral mechanism of the arc channel and shock waves prediction under different discharge conditions.