Air breakdown by perpendicularly intersecting high-power microwave (HPM) is investigated by numerical solution of fluid-based plasma equations coupled with the Maxwell equations. For two coherently intersecting HPM beams, collisional cascade breakdown takes place only when the initial free electrons appear in or arrive at a region of strong electric field, where the electron can be accelerated. At the initial stage of discharge, the filamentary plasma moves along the strong field and forms plasma-filament band. When the plasma-filament band grows long enough, in the vicinity of which the two HPM beams are separated due to its scattering and absorption by plasma. The new plasma-filament bands continue to appear as time increases. It is also found that under the same condition, the plasma region produced by incoherent beams is smaller than by coherent beams.