Deep learning-based methods for deformable image registration are attractive alternatives to conventional registration methods because of their short registration times. However, these methods often fail to estimate larger displacements in complex deformation fields, for which a multi-resolution strategy is required. In this article, we propose to train neural networks progressively to address this problem. Instead of training a large convolutional neural network on the registration task all at once, we initially train smaller versions of the network on lower resolution versions of the images and deformation fields. During training, we progressively expand the network with additional layers that are trained on higher resolution data. We show that this way of training allows a network to learn larger displacements without sacrificing registration accuracy and that the resulting network is less sensitive to large misregistrations compared to training the full network all at once. We generate a large number of ground truth example data by applying random synthetic transformations to a training set of images, and test the network on the problem of intrapatient lung CT registration. We analyze the learned representations in the progressively growing network to assess how the progressive learning strategy influences training. Finally, we show that a progressive training procedure leads to improved registration accuracy when learning large and complex deformations.