Abstract: Two-fluid model and divisional computation techniques were used. The multi-species gas fully N-S equations were solved by upwind TVD scheme. Liquid phase equations were solved by NND scheme. The phases-interaction ODE equations were solved by 2nd Runge-Kutta approach. The favorable agreement is obtained between computational results and PLIF experimental results of iodized air injected into a supersonic flow. Then, the numerical studies were carried out on the mixing of CH₄ and kerosene injected into a supersonic flow with H₂ pilot injection. The results indicate that the penetration of kerosene approaches maximum when it is injected from the second injector. But the kerosene is less diffused compared with the gas fuels. The free droplet region appears in the flow field. The mixing mechanism of CH₄ with H₂ pilot injection is different from that of kerosene. In the staged duct, H₂ can be entrained into both recirculation zones produced by the step and injectors. But CH₄ can only be carried into the recirculation between the injectors. Therefore, initiations of H₂ and CH₄ can occur in those regions. The staged duct is better in enhancing mixing and initiation with H₂ pilot flame.