A new mechanism for the acceleration and production of ions in Z-PINCH discharges, especially plasma focus is presented. Previously, Yousefi et al. [Phys. Plasma 13, 114506 (2006)] studied the multiple compression and PINCH mechanism; they reported that this event can be attributed to the (m=0) type instability, while the subsequent ion and neutron acceleration mechanism was not reported. C ontinuing from previous work, Mizuguchi et al. [Phys.Plasma 14, 032704 (2007)] studied the simulation of high-energy proton production, generated by shock waves in PINCH plasma discharge, by use of a 2D relativistic and fully electromagnetic particle-in-cell code. It was found that protons trapped in the electrostatic potential produced near the shock front, can be accelerated to a few Mev by the surfatron acceleration mechanism. On the other hand, the ring-shape of ion bunches, which is in good agreement with the experimental results, were shown. Now we report another acceleration mechanism for subsequent ion production, which differs from the m=0 instabilities caused by the surfatron acceleration mechanism.