A mathematical model was developed to describe the oscillating amplitude of the plasma arc injected transverse to an external transverse alternating magnetic field. The characteristic of plasma arc under the external transverse alternating magnetic field imposed perpendicular to the plasma current was discussed. The effect of processing parameters, such as flow rate of working gas, arc current, magnetic flux density and the standoff from the nozzle to the workpiece, on the oscillation of plasma arc were also analyzed. The results show that it is feasible to adjust the shape of the plasma arc by the transverse alternating magnetic field, which expands the region of plasma arc thermal treatment upon the workpiece. Furthermore, the oscillating amplitude of plasma arc decreases with decrease of the magnetic flux density. Under the same magnetic flux density, more gas flow rate, more arc current, and less standoff cause the oscillating amplitude to decrease. The researches have provided a deeper understanding of adjusting of plasma arc characteristics.