We study the heavy ion acceleration due to cyclotron interaction with both right- and left-hand polarized MHD waves propagating along the magnetic field in the outward direction in the divergent solar wind. It is shown in test-particle approximation that heavy ions can overcome the gap between the maximum resonant velocity for left-handed waves and minimum resonant velocity for right-handed waves and acquire the average parallel velocity on the order of local Alfven speed relative to the protons.