In the accretion discs, the toroidal magnetic fields and viscous stresses are directly connected to each other, because generation of the large-scale toroidal magnetic fields are produced by the magnetohydrodynamic (MHD) turbulence. Gholipour & Nejad-Asghar have recently shown that the effect of high turbulent viscosity on the Rossby wave instability (RWI) is important, while the effect of low turbulent viscosity can be ignored. In this paper, in addition of turbulent viscosity, we investigate the role of toroidal magnetic field on the non-axisymmetric RWI in the self-gravitating accretion discs. We use a numerical method to investigate stable and unstable modes. The results show that the perturbations of Rossby waves will be damped by both the viscosity and toroidal magnetic field, while the magnetic diffusivity acts vice versa. Also, occurrence of RWI depends on the turbulent magnetic Prandtl number (i.e. ratio of the turbulent viscosity to the turbulent magnetic diffusivity).
