A molecular dynamics simulation with a mixed time-dependent quantum-classical treatment is carried out for the adsorption of HCl on the (0001) surface of ice. All six coordinates of the HCl molecule are considered with two important coordinates, the vibrational coordinate r of HCl and the distance Z between the center of mass of HCl and the ice surface, treated quantally by a grid method with absorbing boundaries. The other coordinates of HCl and all coordinates of the water molecules of ice are treated classically except the intramolecular vibrational motions which are frozen. The results show that treating the two coordinates r and Z quantally is necessary in order to describe the adsorption accurately. The interaction spectra as well as other detailed dynamical information from the simulation are presented. An adsorption energy of 25 kJ/mol is obtained and compared with previous calculation and experiments. The energy transfer between HCl and the ice surface is also calculated. An effort is made to probe the effects of defects of the ice surface on the HCl scattering process.