Two approaches to enhance the output power and current of a flux trapping two staged HMFCG are proposed. Influences of these efforts on its performance is analyzed systematically by using code MFCG-IV, which is a 2D MHD code used to model the dynamic behavior of magnetic flux compression generators with helically wound coils. A series of models have been simulated and analyzed. Simulation results show that the output power of an HMFCG can be enhanced dramatically.