Convolutional Neural Networks have provided state-of-the-art results in several computer vision problems. However, due to a large number of parameters in CNNs, they require a large number of training samples which is a limiting factor for small sample size problems. To address this limitation, we propose SSF-CNN which focuses on learning the 'structure' and 'strength' of filters. The structure of the filter is initialized using a dictionary based filter learning algorithm and the strength of the filter is learned using the small sample training data. The architecture provides the flexibility of training with both small and large training databases, and yields good accuracies even with small size training data. The effectiveness of the algorithm is first demonstrated on MNIST, CIFAR10, and NORB databases, with varying number of training samples. The results show that SSF-CNN significantly reduces the number of parameters required for training while providing high accuracies on the test databases. On small sample size problems such as newborn face recognition and Omniglot, it yields state-of-the-art results. Specifically, on the IIITD Newborn Face Database, the results demonstrate improvement in rank-1 identification accuracy by at least 10%. © 2018 IEEE.