Abstract: Based on the air DBD（Dielectric Barrier Discharge） plasma dynamic model,which has three types of electric particles including positive ion,electron and negative ion,and viscous flow governing equations,low speed air flow with DBD plasmas excited by high alternating current voltage source is numerically simulated by solving the loosely coupled plasma dynamic equations and viscous flow governing equations with finite volume method for their spatial terms and dual-time step method for time development process.The influence of real time step size on DBD plasma development process is investigated in detail.The development process of DBD plasmas and its influence on boundary layer flow around the NACA0015 airfoil are presented.