Quantum 3-sphere is constructed by glueing noncommutative solid tori (quantum disc times circle) along their classical boundaries. The resulting quantum 3-sphere is different from both SUq(2) and the Matsumoto 3-spheres. The irreducible *-representations of its algebra are classified. It is proven that the algebra is a relatively projective U(1)-Galois extension, and the associated projective modules (Hopf line bundles) are discussed. This Hopf-Galois extension is by construction locally trivial.