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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 and infinitely-small growth rate of adiabatic parameter was elucidated. We apply the proposed method to the quantum Hall system with electric and magnetic field in the two dimensional (xy) plane and obtain regularization term, driving potential and driving Hamiltonian to accelerate the system. The driving potential and the driving Hamiltonian to be able to accelerate adiabatic electron dynamics in the ground state trapped in the xy plane and electric field in the x direction and a constant magnetic field in y direction.