One of the most important geometric structures of a protein is the Connolly surface of protein since a Connolly surface plays an important role in protein folding, docking, interactions between proteins, amongst other things. This paper presents an algorithm for precisely and efficiently computing the Connolly surface of a protein using a proposed geometric construct called β-shape based on the Voronoi diagram of atoms in the protein. Given the Voronoi diagram of atoms based on the Euclidean distance from the atom surfaces, the proposed algorithm first computes a β-shape with an appropriate probe. Then, the Connolly surface is computed by employing the blending operation on the atomic complex of the protein by the given probe.