Characteristics of fast-ion losses induced by various magnetohydrodynamic (MHD) instabilities, such as tearing mode (TM), long-lived mode (LLM), and sawtooth crash, have been observed and experimentally investigated in the HL-2A tokamak. To study fastion losses, a new scintillator-based lost-fast ion probe has been developed and used, and an increment of the fast-ion loss rate as the MHD amplitude increase has been measured. Compared with TM and LLM, the fast-ion losses induced by sawtooth crash have a broad range in energy and pitch angle. There may be some interactions between fast ions and magnetic disturbance, which cause the losses with a wide range of energy and pitch angle. During disruptions, the total neutron emission rate drops by ~90% as a result of the strong fast-ion losses. The possible reasons for this phenomenon are the strong magnetic perturbations and the drastic change of the fast-ion transport. In addition, the clear experimental evidence of drastic losses of fast ions during disruptions have been obtained.