Artificial neural networks (ANNs) can outperform the human ability of object recognition by supervised training of synaptic parameters with large datasets. Contrarily to the human brain, however, ANNs cannot continually learn, i.e. acquire new information without catastrophically forgetting previous knowledge. To solve this issue, we present a novel hybrid neural network based on CMOS logic and phase change memory (PCM) synapses, mixing a supervised convolutional neural network (CNN) with bio-inspired unsupervised learning and neuronal redundancy. We demonstrate high classification accuracy in MNIST and CIFAR10 datasets (98% and 85%, respectively) and energy-efficient continual learning of up to 30% of non-trained classes with 83% average accuracy.