The problem of localization of electrons in the presence of electron-phonon interaction in disordered one-dimensional system is studied. In the mean-field approximation, the electron-phonon interaction results in a distorted lattice, the Peierls instability. At the same time, a gap opens at the Fermi level in the electron band. It is known that the scattering of the electrons by the disorder will destroy the lattice distortion and close the gap. However, there is disagreement on the way this happens and on the nature of the resulting electronic states. Recent progress in the experimental and theoretical studies of the one-dimensional organic polymer systems has given a great interest in this problem, and has also provided a suitable model for comparison with the theoretical studies. In this work we present numerical results for the electron density of states, the effective size of the electronic state and the frequency dependent conductivity, and emphasize the mutual effects of the electron localization and the Peierls distortion. We also report on the development based on analytical perturbation theory, and compare some of the available results with those from the numerical studies and experiments.