ABSTRACT The preferential heating of heavy ions in the solar corona and solar wind has been a long-standing hot topic. In this paper we use a one-dimensional hybrid simulation model to investigate the heating of He2+ particles during the parametric instabilities of parallel propagating Alfvén waves with an incoherent spectrum. The evolution of the parametric instabilities has two stages and involves the heavy ion heating during the entire evolution. In the first stage, the density fluctuations are generated by the modulation of the pump Alfvén waves with a spectrum, which then results in rapid coupling with the pump Alfvén waves and the cascade of the magnetic fluctuations. In the second stage, each pump Alfvén wave decays into a forward density mode and a backward daughter Alfvén mode, which is similar to that of a monochromatic pump Alfvén wave. In both stages the perpendicular heating of He2+ particles occurs. This is caused by the cyclotron resonance between He2+ particles and the high-frequency magnetic fluctuations, whereas the Landau resonance between He2+ particles and the density fluctuations leads to the parallel heating of He2+ particles. The influence of the drift velocity between the protons and the He2+ particles on the heating of He2+ particles is also discussed in this paper.