A cosmological Model of viscous modified Chaplygin gas in classical and loop quantum cosmology (LQC) is proposed and a dynamical stability study is investigated. It is shown that the model is consistent with the recent observational data and gives good predictions for the deceleration and state parameters. The model can also predict the time crossing and gives a solution to the coincidence problem. Furthermore, in LQC background, the big bang singularity found in classical cosmology cease to exist and is replaced by a bounce when the Hubble parameter vanishes at the LQC critical energy density.