A high strength, high modulus pitch-based carbon fiber has a crystalline structure in which the presence of the (112) cross-lattice line and the resolution of the diffraction band into the (100) and (101) diffraction lines, which indicate the three-dimensional order of the crystallite of the fiber, are not recognized, and in which the orientation angle (φ) of X-ray structural parameter is not greater than 12° and the stack height (Lc) ranges between 80 and 180°Å. The carbon fiber also has a single-fiber diameter of 5 to 12µm, tensile strength not lower than 3.0 GPa, tensile elastic modulus not smaller than 500 GPa and elongation not smaller than 0.5%.