Efficient particle acceleration is believed to occur in the region around comets. We first review several possibilities for the acceleration process. For a detailed study, we choose the second-order Fermi acceleration. We shortly summarize the results of quasi-linear theory on this acceleration. The theoretical results are then compared with those of test particle simulations, in which particle (ion) motions are traced in hydromagnetic turbulence of given amplitude and spectra. If the energy density of the turbulent magnetic field is less than ≈10% of that of the background magnetic field, the quasi-linear results fit the simulation results well. It is found that nonlinear effects tend to enhance the acceleration rate when the amplitude of turbulence becomes stronger.