The invention discloses an air staged-combustion vertical and horizontal combined arrangement type over fire air system for a tangential boiler. The air staged-combustion vertical and horizontal combined arrangement type over fire air system for the tangential boiler comprises a hearth, a hot air box, a pulverized coal pipeline, a primary air nozzle, a secondary air nozzle, a compact over fire air nozzle, a corner separation over fire air nozzle, a wall type separation over fire air nozzle and the like. According to the system, the tangential boiler is innovated in the conventional hearth height direction on the aspect of the way that over fire air is arranged at the corner, and the purposes of decreasing the excess air coefficient of a main combustion area and reducing NOx generation are realized by arranging corner separation over fire air nozzle and the wall type separation over fire air nozzle which are controlled independently on the upper portion of the main combustion area. By the adoption of the air staged-combustion vertical and horizontal combined arrangement type over fire air system, a sufficient over fire air rate, a reasonable reduction area length, good later-stage intra-boiler mixing and sufficient burn-out time can be guaranteed, smoke remaining rotation and temperature deviation can be effectively eliminated, the requirement for restraining NOx generation and the requirement for promoting pulverized coal to be burnt out are both considered, and the requirements for achieving safety operation of the boiler and being economical and environmentally friendly are met.