Sedimentation in dilute suspensions of charged particles with thin double layers was investigated. The study covered two different cases: sedimentation in polydisperse systems at a large Peclet number and sedimentation in polydisperse systems at a moderate Peclet number. For the first problem, the pair-distribution equation was solved by a regular perturbation method, and it was found that generally speaking the sedimentation coefficient deviates slightly from that at the infinite large Peclet number except the double layer was very thin. For the second problem, a flux-conservation discretization method was utilized in deriving an equivalent difference equation of the pair-distribution equation, which could be solved numerically. We found that the pair-distribution function showed a notable anisotropy in this case. Combing the results of the two problems, we, for the first time, presented an overall picture of the settling behavior of charged particles in which the Peclet number varied from a very small one up to a very large one. The results were found to possess much more diversities than the case of hard spheres.