Electromagnetic plasma accelerators which can produce plasma jets with hypervelocity and high density have been widely used in the fields of nuclear physics and astrophysics. Parallel-rail accelerator, a type of electromagnetic plasma accelerator, is usually used to generate high density and compact plasma jets. The axial movements of plasma in a parallel-rail accelerator operated at different discharge currents and initial pressures are reported in this paper. Based on current truncation, the momentum of the first plasma jet is measured by a ballistic pendulum. The axial movement characteristics and velocity of the plasma during the acceleration phase are diagnosed by magnetic probes and photodiodes. The accelerator is powered by 14 stage pulse forming networks. The capacitor and inductor in each stage are 1.5 μF and 300 nH respectively, yielding a damped oscillation square wave of current with a pulse width of 20.6 μs. Plasma sheath is formed upon breakdown at the back wall insulator surface and subsequently accelerated by Lorentz force towards the open end of the accelerator. A secondary breakdown generally occurs at the starting end of the rail when the current reverses its direction, and then a secondary axial movement of plasma is formed. We focus on the first plasma jet accelerated by the first half-cycle of current. According to the snowplow model, the plasma velocity is proportional to the current and is inversely proportional to the square root of gas initial density or pressure. The axial velocity of the plasma is in a range from 8 km/s to 25 km/s when the discharge current is varied from 10 kA to 55 kA and the initial pressure is varied from 200 Pa to 1000 Pa. The experimental results show that the experimental velocities of the plasma are about 60%-80% of the theoretical result. It is likely that the viscous resistance of the electrode surface acting on the plasma and the mass increase of plasma caused by the electrode ablation are neglected in the snowplow model. The momentum of the first plasma jet is nearly proportional to the integration of the square of current over time, which is consistent with the predictions of the theoretical model. The maximum momenta of plasma jet at different currents appear at average velocities ranging from 13 km/s to 14 km/s when the plasma just moves to the outlet of the rail in the end of the first current pulse. The measured momentum of plasma jet is actually the total momentum of the truncated current waveform. The ratio of the momentum of the first plasma jet to the total measured momentum is about 87%. The momenta of the first plasma jet are in a range from 1.49 g·m/s to 9.88 g·m/s at discharge currents ranging from 21 kA to 51.6 kA. The experimental plasma momentum is about 75% of the theoretical result. These results show that the viscous resistance of rail electrode surface is about 25% of the Lorentz force, and thus leading to a lower value of plasma momentum.