Convolutional sparse representation is an efficient tool for computing sparse representations for entire signals in terms of sums of a set of convolutions with dictionary filters. Unlike representations that are based on overlapping image patches, the convolutional representation optimizes over the entire image, yielding representations that are very sparse both spatially and across the filters. This technique has been successfully applied to natural images, video and speech in tasks as diverse as denoising, classification or superresolution. In this work, we develop a convolutional dictionary learning framework for tomographic reconstruction. We apply the technique to simulated parallel beam tomography data and show that its performance is comparable to the state-of-the-art reconstruction techniques.