Global Positioning System (GPS) satellite receivers provide a world-wide network of phase and group delay measurements. The combination of two-frequency measurements can be used to derive the integral of the electron concentration along each satellite-to-receiver path, a parameter known as the Total Electron Content (TEC). At this stage these slant TEC data are difficult to interpret as they originate from a combination of a temporally changing ionosphere and spatially changing observation geometry. In this paper TEC data are inverted to evaluate the underlying distribution and time evolution of electron concentration. Accordingly, a new three-dimensional, time-dependent algorithm is presented here for imaging ionospheric electron concentration using GPS signals. The inversion results in a three-dimensional movie rather than a static image of the electron-concentration distribution. The technique is demonstrated using, simulated ground-based GPS data from actual measurement geometry over Europe.