A heat accumulating-type burner that operates by alternately repeating heat accumulation and combustion where the heat accumulating element is heated by exhaust gas to accumulate heat therein, and combustion air is passed through the heat accumulating portion to preheat the combustion air by thermal exchange with the heat accumulating element that holds the heat accumulated therein, and the preheated combustion air is used to carry out combustion. The cross-sectional area of the heat accumulating portion at the furnace-inner side is made to be smaller than the cross-sectional area of the heat accumulating portion at the air supply/discharge port side, and in addition, the thickness of the fireproof heat insulating member that covers the heat accumulating portion is made to be thick at the furnace-inner side of the heat accumulating portion, and is made to be thin at the air supply/discharge port side of the heat accumulating portion.