Although deep neural networks (NNs) have achieved state-of-the-art accuracy in many visual recognition tasks, the growing computational complexity and energy consumption of networks remains an issue, especially for applications on platforms with limited resources and requiring real-time processing. Filter pruning techniques have recently shown promising results for the compression and acceleration of convolutional NNs (CNNs). However, these techniques involve numerous steps and complex optimisations because some only prune after training CNNs, while others prune from scratch during training, by integrating sparsity constraints or by modifying the loss function. In this paper, we introduce a new Progressive Gradient Pruning (PGP) technique for iterative filter pruning during training. In contrast to previous progressive pruning techniques, it relies on a novel filter selection criterion that measures the change in filter weights, uses a new hard and soft pruning strategy, and effectively adapts momentum tensors during the backward propagation pass. Experimental results obtained after training various CNNs on benchmark datasets for image classification, object detection and domain adaptation indicate that our PGP technique can achieve a better trade-off between classification accuracy and network (time and memory) complexity than PSFP and other state-of-the-art filter pruning techniques. Code is available on GitHub link: https://github.com/Anon6627/Pruning-PGP.