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It is known that a consensus problem on any connected complete Riemannian manifold can be transformed into the one on its strongly convex balls via the compression–decompression along geodesics. From the viewpoint of interior metrics, this paper mainly provides a consensus protocol for strongly convex geodesic balls, in which the communication can be switching and directed. With the aid of nonsmooth analysis tools on Riemannian manifolds, our analysis shows that all dynamical points involved can achieve consensus in finite time. Meanwhile, the corresponding global algorithm is given, with its application to the consensus problem of rotation attitudes, as well as a case simulation, to demonstrate and verify our proposed techniques. Refereed/Peer-reviewed