Dynamics of an electron in a tightly binding one-dimensional disordered system is studied numerically. The time evolution of wavepackets is traced by the time-dependent Schrodinger equation. The mean square displacement of the packet scaled by the localization length shows a universal time evolution from the ballistic regime to the localized regime in an ordinary disordered system. The time evolution in the modified Bernoulli systems with long-range structural correlation also shows the same universal diffusion.