It is shown that the Gross-Pitaevskii equation has boubble and doublet solutions in three-dimensional cases. The bubble solution corresponds to the limiting vortex ring. It is seen that the limiting vortex ring has a finite vorticity. The three-dimensional doublet solution is obtained by making use of the variational method. It is shown that the doublet solution describes in good apploximation Hill's spherical vortex. The known relation between the strength of the doublet and the momentum of vortex ring follows as a by-product of the present formulation. The density profiles for these two types of solution are spherically symmetric.