Conformation and dynamics of charged polymer chains in counter-ion solvent is studied by a Monte Carlo simulation in two and three dimensions. The nodes of the chains are positively charged while the solvent particles possess negative charge, The concentration of the polymer (p), and the empty sites (p(e)) is varied along with the temperature. Reptation, kink-jump, and a buckling governed by the interaction energy are considered in moving the chain segments. The variation of the root mean square (rms) displacement of the center of mass, and the relaxation of the radius of gyration of the chains with time are studied as a function of polymer concentration and temperature. The rms displacement of the polymer chains exhibits various power laws in different time regimes which depend on the concentration of the chains. Relaxation of the radius of gyration is enhanced on increasing the temperature; the relaxation time seems to decrease on reducing the chain length and increase on increasing the concentration. The motion of solvent particles show subdiffusive behavior which is sensitive to polymer concentration.