Effect of dynamical perturbation on quantum localization phenomenon in one-dimensional disordered quantum system is investigated systematically by a numerical method. The dynamical perturbation is modeled by an oscillatory driving force containing M-independent (mutually incommensurate) frequency components. For M>=2 a diffusive behavior emerges and the presence of finite localization length can no longer be detected numerically. The diffusive motion obeys a subdiffusion law characterized by the exponent α as ξ(t) 2 t α , where ξ(t) 2 is the mean square displacement of the wave packet. With increase in M and/or the perturbation strength, the exponent α approaches rapidly to 1 which corresponds to the normal-diffusion. Moreover, the space(x)-time(t) dependence of the distribution function P(x,t) is reduced to a scaled form decided by α and an another exponent β such that P(x,t)~exp{-const.(|x|/t α / 2 ) β }, which contains the two extreme limits, i.e., the localization limit (α=0,β=1) and the normal-diffusion limit (α=1,β=2) in a unified manner.