To find an ignition and combustion control strategy in a gasoline-fueled HCCI engine equipped with the BlowDown SuperCharging (BDSC) system which is previously proposed by the authors, a one-dimensional HCCI engine cycle simulator capable of predicting the ignition and heat release of HCCI combustion was developed. The ignition and the combustion models based on Livengood-Wu integral and Wiebe function were implemented in the simulator. The predictive accuracy of the developed simulator in the combustion timing, combustion duration and heat release rate was validated by comparing to experimental results. Using the developed simulator, the control strategy for the engine operating mode switching between HCCI and SI combustion was explored with focus attention on transient behaviors of air-fuel ratio, A/F, and gas-fuel ratio, G/F. The simulation result showed that the one-step variations in the amount of recharged EGR gas and G/F can be attained by activation or deactivation of the EGR valve lift with the BDSC system. It is considered that this one-step variation in G/F allows the one-step transition from the HCCI operation to the SI operation with small torque fluctuation. However, in the combustion mode transition from SI to HCCI, the combustion timing during the transient HCCI combustion was excessively advanced. The excessively advanced ignition timing leads to the increase in in-cylinder pressure rise rate, dP/dθ. In the strategies examined in the present study, only intake throttle valve, exhaust throttle valve and EGR valve lift switching were used to control mixture conditions in terms of A/F and G/F during combustion mode transition. The results obtained suggest that additional devices to control mixture conditions during the combustion mode transition are necessary to attain the smooth transition from SI to HCCI combustion.