It is now widely accepted that large solar energetic particle (SEP) events are associated with coronal mass ejection (CME)-driven shocks. Here, particles are often accelerated to approximately MeV energies (and perhaps up to GeV energies) at shock waves driven by CMEs. In this paper, on the basis of our earlier work, we present a detailed model which calculates the acceleration of heavy ions at CME-driven shocks and their subsequent propagation in the interplanetary medium. The CME-driven shock is followed numerically using the two-dimensional ZEUS code. At the shock front and upstream of the shock, the coupled system of streaming protons and stimulated upstream turbulence (assuming the form of Alfv¿n waves) is considered and the diffusion coefficient of the energetic ions and the stimulated wave intensity is evaluated self-consistently. The particle diffusion coefficient is then used to determine the maximum momentum of energetic ions. The ion spectra at the shock front are obtained by adopting the steady-state solution of the transport equation. Across the shock front, the upstream turbulence is amplified and the particle diffusion coefficient is further decreased. Energetic particles in the downstream region convect with the solar wind, cool adiabatically, and diffuse. These effects are followed using a shell model. Particles diffuse ahead of the shock front, can escape and propagate in the interplanetary medium subject to pitch angle scattering. The transport of these particles is followed using a Monte-Carlo code. Two shocks, one strong and one weak, are considered. Time intensity profiles and particle spectra at various times are obtained for two groups of ions, corresponding to Fe and CNO particles. These results will be helpful on understanding in situ observations at 1 AU made by spacecraft such as ACE and Wind.