Plasma convection in the high-latitude ionosphere provides important information about magnetosphere-ionosphere-thermosphere coupling. In this study we estimate the along-track component of plasma convection within and around the polar cap, using electron density profiles measured by the three Swarm satellites. The velocity values estimated from the two different satellite pairs agree with each other. In both hemispheres the estimated velocity is generally anti-sunward, especially for higher speeds. The obtained velocity is in qualitative agreement with Super Dual Auroral Radar Network data. Our method can supplement currently available instruments for ionospheric plasma velocity measurements, especially in cases where these traditional instruments suffer from their inherent limitations. Also, the method can be generalized to other satellite constellations carrying electron density probes.