Abstract: Plasma arc behavior plays a decisive role in the microstructure and properties of welded joint. Therefore, it is of great significance to study characteristic of gas focusing plasma for guiding gas focusing plasma arc welding advanced material and improving welded joint properties. The mathematical model of arc in gas focusing plasma arc welding as a new welding process, is developed based on fluid dynamics theory and electromagnetic theory. The model is conducted on software ANSYS Fluent with further development by C program language. The temperature distribution, velocity filed, potential of plasma arc are calculated quantitatively. And influence of focusing gas on arc temperature, plasma velocity and arc voltage is analyzed. Plasma temperature outside of nozzle is focused by focusing gas, while plasma temperature inside of nozzle is basically unchanged with or without focusing gas. Plasma velocity distribution both inside and outside of nozzle has no significant changes with focusing gas. Arc voltage in gas focusing plasma arc welding is larger than that in traditional plasma arc welding with the same welding current. Under the same condition on welding current, arc penetrability in gas focusing plasma arc welding will increase compared with traditional plasma arc welding.