For investigating the mechanism of high power microwave flashover and breakdown on dielectric surface with outgassing, firstly, the theoretical modeling is put forward, including dynamic equations, particle-in-cell (PIC) method, secondary emission, Monte-Carlo collision (MCC) method and outgassing model. Secondly, based on the theoretical modeling, the 1D3V PIC-MCC code is programmed by authors. By using this code, the flashover and breakdown on dielectric surface with weak and strong outgassing course under different gas moving velocities are studied numerically. The numerical results are concluded in the following. The flashover and breakdown on dielectric surface are caused by continuous increase of deposited power. For weak outgassing, multipacting is dominant. As outgassing coefficient increases, multipacting is promoted by ionization collision. The typical phenomena are the increases of space-charge field, average energy of surface-collision electrons and the number of surface-collision electrons. Here, the surface-collision electrons are caused by multipacting mostly. With the increase of gas molecule velocity, ionization course is suppressed by gas pressure decreasing near to the dielectric surface. For strong outgassing, ionization collision is dominant. As outgassing coefficient increases, the number of ions increases exponentially with ionization frequency increasing, multipacting is suppressed by ionization collision. The typical phenomena are the negative value of space-charge field on dielectric surface, the decrease of average energy of surface-collision electrons, and the exponential increase of surface-collision electrons caused by ionization collision near to dielectric surface. Here, the surface-collision electrons are caused by ionization mostly. With the increase of gas molecule velocity, the depth of gas is enlarged, thereby promoting the ionization collision.