Summary: We investigate the property of a singularity which is formed by the spherical collapse of pure radiation from past null infinity, in terms of the congruence of null geodesics in the Vaidya spacetime. When the initial increase of mass due to the inflow of radiation is not so fast, the so-called shell-focusing singularity appears at the center. We present a class of examples in which such a singularity becomes globally naked. This is a counterexample to the cosmic censorship hypothesis.