A carburizing steel having the following chemical composition: C: 0.1 to 0.25%, Si: 0.2 to 0.4%, Mn: 0.3 to 0.9%, P: 0.02% or less, S: 0.001 to 0.15%, Cr: 0.5 to 0.9%, Mo: 0.15 to 1%, Al: 0.01 to 0.1%, B: 0.0005 to 0.009%, N: less than 0.006%, and the balance of Fe and incidental impurities, wherein % is on a weight basis. Also disclosed are a method for the manufacture of the carburizing steel, parts of constant velocity universal joints for drive shafts made of the carburizing steel, as well as a method for the manufacture of such parts. The carburizing steel may further contain Ni: 0.3-4.0%, and one or more elements selected from the group consisting of Ti, Nb, V and Zr: 0.01-0.3% for each. The parts of constant velocity universal joints for drive shafts are manufactured using the carburizing steel of the present invention as a material. When they are carburized and quenched, they exhibit a surface hardness (Hv) of 650-800, core hardness (Hv) of 250-450, and carburized case depth of 0.2-1.2 mm.