There is an important relationship between gradient of pressure and the bootstrap current. Due to the alpha (a gradient scale of pressure) is the essential condition to trap discrete Alfven eigenmodes (alpha-induced Alfven eigenmodes, namely alpha TAEs), here, we focus on the relationship between alpha TAEs and bootstrap current with a magnetohydrodynamic (MHD) simulation code and a gyrokinetic-MHD hybrid simulation code in two typical scenarios in ITER, and compare these typical scenarios with two ordinary scenarios about physical characteristics of discrete Alfven eigenmodes. These discrete Alfven eigenmodes are always lying in the region of high bootstrap current. However, they are not corresponding absolutely in pure radio frequency scenario (one of typical scenarios) because of large-alpha. Moreover, we illustrate the multiple branches of discrete Alfven eigenmodes in those typical scenarios, and find high-order modes trapped by the lower potential well. Discrete Alfven eigenmodes exist widely in ITER scenarios with bootstrap current. However, discrete Alfven eigenmodes are quasi-marginally stable in MHD description and could be readily destabilized by energetic particles in hybrid simulation via wave-particle resonances.