The role of scatter in a cone-beam computed tomography system using the therapeutic beam of a medical linear accelerator and a commercial electronic portal imaging device (EPID) is investigated. A scatter correction method is presented which is based on a superposition of Monte Carlo generated scatter kernels. The kernels are adapted to both the spectral response of the EPID and the dimensions of the phantom being scanned. The method is part of a calibration procedure which converts the measured transmission data acquired for each projection angle into water-equivalent thicknesses. Tomographic reconstruction of the projections then yields an estimate of the electron density distribution of the phantom. It is found that scatter produces cupping artefacts in the reconstructed tomograms. Furthermore, reconstructed electron densities deviate greatly (by about 30%) from their expected values. The scatter correction method removes the cupping artefacts and decreases the deviations from 30% down to about 8%.