Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction methods. Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times. As a possible solution to these restrictions we propose a multi-scale learned iterative reconstruction algorithm that computes iterates on discretisations of increasing resolution. This procedure does not only reduce memory requirements, it also considerably speeds up reconstruction and training times, but most importantly is scalable to large scale inverse problems, like those that arise in 3D tomographic imaging. Feasibility of the proposed method to speed up training and computation times in comparison to established learned reconstruction methods in 2D is demonstrated for low dose computed tomography (CT), for which we utilise the data base of abdominal CT scans provided for the 2016 AAPM low-dose CT grand challenge.