A carbon fiber of a high tenacity and a high modulus of elasticity having a fiber diameter of 1 to 6 (my)m, a strand tenacity of 430 kg/mm2 or more, a strand modulus of elasticity of 28 ton/mm2 or more and a density of 1.755 g/cm3 or more, and a process for producing the same. The above-mentioned carbon fiber has extremely useful properties as a raw material for composite materials to be used not only for sporting goods such as fishing rods or golf clubs but also in aerospace industries.