Gradual solar energetic particle events using data observed by EPAM (Electron, Proton, and Alpha Monitor), SWEPAM (Solar Wind Electron, Proton and Alpha Monitor) and Magnetic Field Experiment (MAG) on the ACE are studied. The energetic particle events are classified in four types according to the variance in the flux, the characteristic duration time of the events and the maximum energy of the accelerated particles. We perform the modeling of typical events by using numerical simulations for two types. We apply the stochastic differential equation method coupled with the particle splitting to diffusive acceleration, and obtain the energy spectrum and the spatial distribution of the accelerated particles. The relation between the different classes of the events and injection model is discussed.