Coaxial gun can produce high-speed and high-density plasma jet and has some potential applications in many research areas such as space thruster, space debris impact simulation, nuclear fusion, and material processing. The coaxial gun is usually composed of a pair of coaxial cylindrical and hollow electrodes. The pulsed discharge of coaxial gun has two discharge modes, i.e., deflagration mode and pre-fill mode. Compared with the pre-fill mode, deflagration discharge mode can induce a plasma jet with few impurities, high collimation, and fast speed. In this paper, the effect of gas injection mass and discharge voltage on the discharge characteristic of deflagration mode are studied with electrical and optical diagnosis including the emission spectrum, plasma velocity and discharge current measurements. The experimental results show that when the gas injection mass is relatively low, such as 1.4 mg, many plasma clusters eject from the muzzle. As the gas flowing into the coaxial gun bottom increases, the plasma density increases and the jet velocity decreases. Eventually, when the gas injection mass increases to 2.6 mg, one cluster of plasma is found and ejects from the muzzle of the gun. In the discharge process, as a small quantity of gas flows into the bottom of the coaxial gun through the electromagnetic valve continuously, new current paths will be generated at the bottom of the coaxial gun and move forward. This results in the observation of multiple plasma jet at the exit of the coaxial gun. It is noted that the plasma densities are different for different gas mass flowing into coaxial gun bottom, but the currents have little effect in the first discharge half cycle due to the small plasma inductance in discharge circuit. Meanwhile, the plasma characteristics under different voltages with the fixed gas mass of 2.6 mg flowing into the coaxial gun bottom are experimentally measured. The results show that the plasma density and speed increase with voltage increasing, which is attributed to the stronger discharge current and larger self-induced Lorentz force. More neutral particles can be ionized into plasma with discharge voltage increasing, and the transport speed becomes faster under the enhanced force. In addition, the multiple ionization phenomena are observed again when the discharge voltage increases from 5 kV to 8 kV. This study provides an insight into how to better apply the coaxial gun discharge plasma to practical engineering field. The article further verifies the phenomenon of multiple discharges at the bottom of the coaxial gun by changing the charging capacitance and analyzing the magnetic probe signals.