A new kind of accelerating flat model with no dark energy that is fully dominated by cold dark matter (CDM) is investigated. The number of CDM particles is not conserved and the present accelerating stage is a consequence of the negative pressure describing the irreversible process of gravitational particle creation. A related work involving accelerating CDM cosmology has been discussed before the SNe observations [Lima, Abramo & Germano, Phys. Rev. D53, 4287 (1996)]. However, in order to have a transition from a decelerating to an accelerating regime at low redshifts, the matter creation rate proposed here includes a constant term of the order of the Hubble parameter. In this case, H0 does not need to be small in order to solve the age problem and the transition happens even if the matter creation is negligible during the radiation and part of the matter dominated phase. Therefore, instead of the vacuum dominance at redshifts of the order of a few, the present accelerating stage in this sort of Einstein-de Sitter CDM cosmology is a consequence of the gravitational particle creation process. As an extra bonus, in the present scenario does not exist the coincidence problem that plagues models with dominance of dark energy. The model is able to harmonize a CDM picture with the present age of the universe, the latest measurements of the Hubble parameter and the Supernovae observations. PACS numbers: 95.35.+d,95.30.Tg