The invention relates to a chain-grate boiler and a burning method. The chain-grate boiler comprises a boiler body, an induced draft fan, a circulation fan, a primary fan and an air supply bin; primary air pumped from natural air is fed into the air supply bin through the primary fan, and therefore drying, burning and burnout of coal are promoted; and circulation smoke pumped from total smoke passing through the induced draft fan is fed into a burning air supply bin in the air supply bin through the circulation fan, and generation of NOx is restrained. Furthermore, part of the circulation smoke pumped from the total smoke passing through the induced draft fan is fed into a backwards-arched air distribution opening through the circulation fan, mixing of smoke in a hearth is strengthened, burning of fuel is promoted, and the burning efficiency of the chain-grate boiler is improved. By means of the burning method of the chain-grate boiler, generation of the NOx is correspondingly restrained, and the burning efficiency of the chain-grate boiler is improved.