TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: A part of the carbon fibers has a component that connects the thin piece bodies adjoining in a laminating direction of the other thin piece body. The thin piece bodies are disposed so that ends of the thin piece bodies are deviated in the laminating direction. The carbon fibers have an average fiber length of less than 1 mm. In carbon fiber structure an orienting component of the carbon fibers in a vertical direction to the surface direction of the carbon fiber structure is present continuously in the vertical direction. The carbon fiber structure has a bulk density of at least 1.2 g/cm3. In the method the average fiber length of the carbon fiber is smaller than size of an opening of the porous die face. Preferred Method: The filtering step is through a suction filtering. In step (a) a first binder is precursor component of the matrix and a second binder is a component for coupling the carbon fibers and first binder in the liquid and adding an aggregating agent to aggregate the carbon fibers and first and second binders to form the flocks. The step (c) is heat compression step performed in an autoclave in a state where the laminate of flocks is covered by a film. EXAMPLE - Polyacrylonitrile based carbon fibers (7 mu m) were prepared. A sizing agent was coated on fiber surface and calcined at 550 degrees C, and removed. The carbon fibers were dispersed in water and pulverized (150 mu m), followed by dehydration and drying. Then, carbon fibers were heated with organic material powder. The carbon fibers were thrown into water and dispersed, while stirring for 3 minutes. Bell Pearl S890 (RTM: Phenol resin) (200 parts by mass), Percol 292 (RTM: Cationic aggregating agent) (0.3 parts by mass) and latex (5 parts by mass) were added to carbon fibers (100 parts by mass) and the mixture was stirred to obtain flocks. Flocks were sucked from cylindrical die to obtain cylindrical laminate. Wire net-free cylindrical die was inserted into the laminate. The resultant laminate was placed in autoclave and pressurized at 150 degrees C and at a pressure of 2 MPa pressure for 2 hours. The die of the laminate was removed, and the resultant laminate was heated at 70 degrees C/hour and at 550 degrees C, the laminate was cooled and hydrocarbon gas was purged. The laminate was degreased and impregnated with pitch at 200 degrees C and at a pressure of 4 MPa. The laminate was again degreased. The laminate was calcined at 150 degrees C/hour and at 2000 degrees C, the laminate was cooled and carbon powders were added to obtain cylindrical carbon fiber structure (having inner diameter of 1000 mm and thickness of 25 mm).