We present a real-space, polynomial-expansion approach to electron dynamics in nanostructured semiconductors. The Chebyshev expansion method is employed for efficient calculation of timeevolution of single-electron wave function. Details of the formulation are described. The method is applied to the electron transport in nanostructured semiconductors such as Si nanowires. The mean-square displacement and diffusivity of electron in Si chains are obtained as functions of length of the chains. The results show clearly ballistic behavior of electron in the pure Si chain.