We report a new phenomenon that particles are selectively entrained along the corners of a straight rectangular microchannel according to their deformabilities under viscoelastic flows of a polymer solution. The mechanism behind this phenomenon is elucidated by the competition between the wall lift force induced by the particle deformability and the elastic force of the medium at the corners. On the basis of these findings, we devise a novel label-free deformability-selective cell-separation method, which achieves the high-purity separation of rigid particles and rigidified red blood cells (RBCs) from fresh RBCs in a single step, without any active components such as an electric force or sophisticated channel design. Furthermore, our novel method can be used directly to isolate white blood cells (WBCs) from diluted whole blood with a high enrichment ratio (>300) by utilizing difference in cell deformability.