We consider a late decaying dark matter model in which cold dark matter begins to decay into relativistic particles at a recent epoch (z ≤ 1). A complete set of Boltzmann equations for dark matter and other relevant particles particles is derived, which is necessary to calculate the evolution of the energy density and density perturbations. We show that the large entropy production and associated bulk viscosity from such decays leads to a recently accelerating cosmology consistent with observations. We determine the constraints on the decaying dark matter model with bulk viscosity by using a MCMC method combined with observational data of the CMB and type Ia supernovae.