Let Mm be a m-dimensional submanifold in the n-dimensional unit sphere Sn without umbilic point. Two basic invariants of Mm under the Mobius transformation group of Sn are a 1-form Φ called Mobius form and a symmetric (0,2) tensor A called Blaschke tensor. In this paper, we prove the following rigidity theorem: Let Mm be a m-dimensional (m≥3) submanifold with vanishing Mobius form and with constant Mobius scalar curvature R in Sn, denote the trace-free Blaschke tensor by \(\). If \(\), then either ||A||≡0 and Mm is Mobius equivalent to a minimal submanifold with constant scalar curvature in Sn; or \(\) and Mm is Mobius equivalent to \(\) in \(\) for some c≥0 and \(\).