The invention discloses a low-NO<x> efficient chain grate furnace with a function of distributing air by area in the width direction of a grate. On the basis that air enters from the two sides of theposition below the grate, a primary air chamber is divided into a grate left air chamber body, a grate middle air chamber body and a grate right air chamber body by subarea partition plates in the width direction of the grate, the grate left air chamber body, the grate middle air chamber body and the grate right air chamber body are three transverse small air chamber bodies, inlets of all the transverse small air chamber bodies are provided with adjustable air doors, flow equalization plates are arranged in the transverse small air chamber bodies, and accordingly, the condition for distributing the air by area in the width direction of the grate is built. The effect that based on the existing technology, air supply of the middle of a coal seam is strengthened, and air supply of the two sides of the coal seam is appropriately reduced, thus, primary air is relatively uniformly distributed in the width direction of the grate, the situation that the air pressure, the air volume and the airflow penetrating power of all the areas of the coal seam are consistent with the air / coal diffusive combustion condition is achieved, surplus escaped air above the coal seam is little and uniform, accordingly, the problem that when NO<x> discharge is controlled through low-oxygen combustion, coal is stacked in the middle of the grate, and as a result, the burnout effect is poor is solved, the efficient low-oxygen combustion condition of the grate areas is built, and the effects of being good in burnout, low in smoke exhaust loss and small in NO<x> generation amount are achieved.