Discharge current oscillations, especially a frequency range of several tens kilohertz, have been a significant problem in Hall thrusters from the viewpoint of electromagnetic interference because a discharge-current frequency and amplitude are unpredictable. A pulsating boost chopper power supply (chopper PS) has been developed to adjust a discharge-current frequency to a chopping frequency of the chopper PS. In our previous studies, for both SPT and TAL-type Hall thrusters, the chopper PS shifted the oscillating frequency to the chopping frequency and successfully suppressed the amplitude of the discharge current. However, the discharge-current spectrum showed a sharp peak on the chopping frequency. In this study, a spread spectrum was applied to the pulse signal, which switches the field-effect transistor of the chopper PS, with the aim to reduce the spectrum intensity on the chopping frequency. As a result, the spectrum peak was attenuated with improved thrust performance and suppressed discharge-current amplitude and ion wall loss.