A support structure (32) for supporting checker bricks (5) of a hot blast stove, the structure (32) comprising slope bricks (7) for supporting the checker bricks (5) and support bricks (6) for supporting the slope bricks (7). The slope bricks (7) have a body (70) and sloped passages (75), which communicate with the through holes (54) of the checker bricks (5) and which open onto the side surface of the body (70). The slope bricks (7) are arranged along imaginary sloped surfaces that partition the interior of the hot blast stove into an upper section and a lower section. Between the slope bricks (7) and the support bricks (6), horizontal passages (35) that communicate with the sloped passages (75) are formed.