The coaxial gun discharge, used as plasma jet with high density and velocity, has a wide variety of applications such as plasma space propulsion, simulation experiment of thermal transient events in the International Thermonuclear Experimental Reactor, plasma refueling for fusion reactors and a laboratory scale platform for studying astrophysical phenomena. The plasma produced in the coaxial gun can be accelerated by self-induced Lorentz force, and the ionization in the transport process can be based on " snow-plow model” in which a coaxial current sheet moves forward and sweeps a large amount of the gas between two electrodes to cause the plasma dump. Based on the measurements of discharge current, voltage, photocurrent and magnetic signal, the experimental investigation on the characteristics of plasma motion and current sheet channel distribution in the gun operated under different discharge conditions and various pressures is carried out. In this paper, it is emphasized to explore the electrical and dynamic properties about plasma in the first half-cycle of current. The results show that the plasma velocity increases with the increase of the current amplitude, and that the transport distance is proportional to the axial kinetic energy of ions when the pressure is fixed at 10 Pa and discharge current is adjusted from 35.7 kA to 69.8 kA. Moreover, in the case of high current, the plasma jet from the nozzle tends to form a new current path at the bottom of the gun. However, when the discharge current is fixed at 49.8 kA and the gas pressures range from 5 Pa to 40 Pa, the plasma motion velocity and transport distance are continuously reduced. Meanwhile, it is not found that new current paths are generated at the bottom of the coaxial gun under high pressure. The generation of the new current path is relevant to the channel impedance formed by more charged particles left at the bottom of the gun and neutral particles leaking from current sheet during discharge. Besides, a multiple discharge phenomenon is presented in experiment and the secondary discharge breakdown position occurs at the head of the electrode when the current is reversed to a positive value. Therefore, this study provides a reasonable choice of electrical parameters to obtain optimal plasma characteristics during the discharge of the coaxial gun.