A new tomographic reconstruction algorithm is presented, termed direct least-squares reconstruction (DLSR), which solves the well known parallax problem in X-ray-scattering-based experiments. The parallax artefact arises from relatively large samples where X-rays, scattered from a scattering angle 2θ, arrive at multiple detector elements. This phenomenon leads to loss of physico-chemical information associated with diffraction peak shape and position (i.e. altering the calculated crystallite size and lattice parameter values, respectively) and is currently the major barrier to investigating samples and devices at the centimetre level (scale-up problem). The accuracy of the DLSR algorithm has been tested against simulated and experimental X-ray diffraction computed tomography data using the TOPAS software.