Given a protein, it is often necessary to study its geometric and physicochemical properties for studying its structure and predicting funtions of a protein. In this case, a connolly surface of a protein plays important roles for these purpose. A protein consists of a set of amino acids and a set of atoms comprise an amino acide. Since an atom can be represented by a hard 3D sphere in van der Waals model, a protein is usually modeled as a set of 3D spheres. In this paper, we present the algorithm for computing a connolly surface using Euclidean Voronoi diagram atoms of a protein. The algorithm initially locates the exterior aotms of a protein where connolly surface patches exist and computes the patches by tracking their boundary curves. Since a Euclidean Voronoi diagram is uniquely defined independent of probe radius different from other geometric structures, the connolly surfaces defined by probes of different radii can be computed without re-computing the Euclidean Voronoi diagram.