The one-dimensional polyconjugated chains of biomolecules are chosen for study. The band theory of the pi-electrons in polymers is reviewed and the experimental results of electric conduction in biomolecular systems are discussed. The migation of charges, especially that of holes which is considered to be important in both conduction phenomena and physical processes of radiation damage, .is studied in a simplified mode]. We use the Wannier function to represent the access charge, say a hole, made initially at some localized region and the time evolution is described by the time - dependent Wannier function. It is shown that the hole or the access electron in the polyconjugated chain of a protein or a DNA macromolecule, will spread out after some time duration t > To , where To~ 10 to the -15 sec for most cases. And the r.m.s. velocity of spreading is approximately equal to the group velocity in the band conduction, it is estimated that vrms = 10 to the 6th ~10 to the 7th cm/sec. The probability of finding the access charge at n unit cells away from the initial place is Pn = |Jn (2Bt/h)|2 where is the Bessel function of first kind and of order n. The effects neglected in this simplified treatment and their expected importances for intra-molecular charge transfer processes are discussed briefly.