According to the tight-binding model of the single electron, we establish a one-dimensional random binary solid model for DNA molecules. Using the transfer-matrix approach, we calculate numerically the localization length and the conductivity of a DNA sequence with 50000 nucleotides base pairs. The results show that the random DNA sequence is an insulator with very small conductivity, that the localization length and conductivity strongly depend on energies, and there exist greater localization lengths at the band center than at the band edge, which implies there is higher conductivity at the band center. The results also show the localization lengths are affected by disorder degrees to some extent and decrease with the increasing of the degree of disorder for all energies. Especially with finite-size DNA sequence, the localization length and conductivity have obvious effect on nucleotide base pairs’ mol percentage.