The stability of toroidal Alfven eigenmodes (TAEs) is presented for steady state plasmas in the JT-60 Super Upgrade (JT-60SU). Studies are carried out by using the ACCOME code for calculating self-consistent MHD equilibria and by using the NOVA-K code for analysing the TAE stability. Characteristics of the TAE stability are obtained for non-inductive steady state plasmas (3 MA/3 T) with a large bootstrap current and a 500 keV neutral beam (NB) current. Above the density value corresponding to VhVA~1, the TAE becomes unstable owing to the large pressure gradient, ΔPh, and the large β of the hot particles, (βh). Here, VhVA is the ratio of the hot particle velocity to the Alfven velocity. As the density and the temperature increase, the bootstrap current increases so that the NB power required for the current drive decreases. Consequently, both ΔPh and (βh) decrease and the TAEs are stabilized by ion Landau damping. In the high current and high toroidal field plasma (10 MA/6.25 T) case, because ΔPh is small, owing to high density, and (βh) is small, owing to high toroidal field, the TAE is stable for low n to medium n (⩽15)