To perform a flame-resistant treatment on a precursor fiber strand by sending hot air to a heat treatment chamber (2) through a hot air blowing nozzle (4) in a direction parallel to a running direction of a precursor fiber strand (10). The hot air blowing from the hot air blowing nozzle (4) passes through a porous plate and a rectifying member that satisfy the following conditions (1) to (4), wherein the conditions are set as follows: (1) A/B≧4.0; (2) 0.15≦α≦0.35; (3) 0≦B−d≦20; and (4) 80% or more of an area of one opening of the porous plate when causing facing surfaces of the porous plate and the rectifying member to overlap each other is included in one opening of the rectifying member, A indicating a hot air passage distance (mm) of the rectifying member, B indicating a horizontal maximum distance (mm) of one opening of the rectifying member, α indicating a rate of hole area of the porous plate, and d indicating an equivalent diameter (mm) of the porous plate. Accordingly, it is possible to provide a parallel stream type flame-resistant heat treatment furnace having exhibiting the uniform heat transfer performance throughout the inside of the heat treatment chamber by preventing the blockage of the nozzle caused by a silicone compound generated inside the heat treatment chamber even in the hot air blowing nozzle having a simple structure.