We study a scheme of accelerated adiabatic quantum dynamics. This scheme was originally proposed by Masuda-Nakamura. The strategy of combining two opposite idea: infinitely-large time-magnification factor (ᾱ) and infinitely-small growth rate (ɛ) of adiabatic parameter was elucidated. We apply the proposed method to the Hall system with electric and magnetic field and obtain regularization term, driving potential VFF and driving Hamiltonian HFF to accelerate the system. The driving potential VFF and the driving Hamiltonian HFF to be able to accelerate adiabatic electron dynamics in the ground state trapped in the plane xy and electric field in the x direction and a constant magnetic field in y direction.