The invention provides a multi-dimensional air staging low-NOx combustion system and an arrangement method. The stable combustion capability and the pulverized coal combustion efficiency of a boiler during the unit low-load operation stage are not taken into consideration in an existing staging NOx combustion method. During the unit low-load operation stage, if concentrated phase pulverized coal air flow deflects towards the fire-side water-cooled wall at wide angle, the problems that boiler combustion gets worse, slag is agglomerated on the water-cooled wall of the boiler and high-temperaturecorrosion becomes more severe due to reverse rotation of the boiler combustion tangential circle occur very easily. The multi-dimensional air staging low-NOx combustion system comprises main combustors and two-stage over- fire air combustors. The main combustors are arranged at the four corners of a boiler furnace (25) correspondingly. An included angle alpha formed between the central axis (22)of each main combustor and the water-cooled wall of the boiler furnace is 40-43 degrees. A set of secondary air nozzles and primary air nozzles arranged in a spaced mode are arranged on each main combustor.