Stochastic acceleration of 3 He and 4 He from a thermal background by parallel propagating turbulent plasma waves with an assumed power-law spectrum of the wavenumber is studied. In the model the acceleration rate is reduced considerably when the interaction is dominated by one of the several resonant wave modes. At low energies, this happens for 4 He but not for 3 He. As a result, the acceleration of 4 He is suppressed by a barrier below~ 100 keV nucleon-1, and there is a prominent quasi-thermal component in the 4 He spectra, while almost all 3 He ions are accelerated to high energies. The model accounts for the large enrichment of 3 He observed in impulsive solar energetic particle events and fits the spectra of both ions with reasonable plasma parameters. This study also indicates that the acceleration, Coulomb losses, and diffusive escape of particles from the acceleration site all play important roles in shaping the ion spectra, which may explain the varied spectral shapes observed recently by the Advanced Composition Explorer. However, for further quantitative analysis and to apply the model to the acceleration of other ions, the generation and evolution of the turbulence need to be addressed.