This paper attempts to predict the noise emission characteristics of a turbulent argon thermal-plasma jet issuing into ambient air. The flow, temperature and concentration fields and turbulence characteristics of the turbulent plasma jet are computed at first, and then the noise emission from the plasma jet to a sideline far-field observer is calculated using the approach proposed by Fortune and Gervais (AIAA J. 37(1999)1055) for predicting the noise emission from a turbulent, hot but non-ionized, air jet after some modification. The diffusion of ambient air into the turbulent argon plasma jet is handled using the turbulence-enhanced combined-diffusion-coefficient method. Velocity fluctuation correlations (aerodynamic noise source) in the plasma jet are calculated still using the K-epsilon two-equation turbulence model, but the temperature-velocity fluctuation correlations (entropic noise source) within the jet are calculated by solving a second-order turbulent Reynolds heat-flux transport equation in order to better deal with the contribution of temperature fluctuation to the noise emission. It is shown that among the contributions of aerodynamic noise source, entropic noise source and their mixed effect, the entropic noise source (i.e. the temperature-velocity fluctuation correlations) is dominant for the noise emission from the turbulent plasma jet to the sideline observer. The noise intensity increases with increasing plasma jet temperature or velocity. The predicted noise frequency spectrum characteristics and noise intensity levels are shown to be reasonably consistent with available experimental data.