Taking aluminum dust as an example, the generation and acceleration of shock wave induced by weak Ignition in dust suspension in a long horizontal combustion tube have been studied theoretically and numerically. Two fluid model and TVD technique are used to calculate the flow field of gas phase and particle phase and Arrihenius law and k-ε model considering the near wall turbulent are used to calculate the chemical reaction. The wall turbulent plays a important role in the flame acceleration and combustion induce shock process. Simulated results reveal the innate character from compressive wave to shock wave in combustible dust suspension and the flow field parameter distribution. The simulated and measured results are compared with a good agreement.