Plasma, in which many biomarker molecules are suspended, is essential for early diagnosis and medical treatments for various diseases. While blood cells can be easily removed by centrifugation, platelet removal from plasma is comparably difficult due to small size and density similar to plasma. As platelets in plasma may interfere with detection systems, platelet removal is required for precise diagnostics. Here, we propose an elasto-inertial microfluidic device for efficient removal of platelets to separate pure plasma. Based on a co-flow of Newtonian and viscoelastic fluids, we utilize both inertial and elastic forces to translocate the platelets across the co-flow interface for pure plasma separation in a high-throughput, dilution-free manner. We carefully designed the microchannel based on theoretical and numerical analysis and experimentally demonstrated high-purity plasma separation with impurity < 7%. We expect that the proposed method serves as a promising approach for plasma separation for various clinical applications.