We describe a novel spiking neural network (SNN) for automated, real-time handwritten digit classification and its implementation on a GP-GPU platform. Information processing within the network, from feature extraction to classification is implemented by mimicking the basic aspects of neuronal spike initiation and propagation in the brain. The feature extraction layer of the SNN uses fixed synaptic weight maps to extract the key features of the image and the classifier layer uses the recently developed NormAD approximate gradient descent based supervised learning algorithm for spiking neural networks to adjust the synaptic weights. On the standard MNIST database images of handwritten digits, our network achieves an accuracy of 99.80% on the training set and 98.06% on the test set, with nearly 7x fewer parameters compared to the state-of-the-art spiking networks. We further use this network in a GPU based user-interface system demonstrating real-time SNN simulation to infer digits written by different users. On a test set of 500 such images, this real-time platform achieves an accuracy exceeding 97% while making a prediction within an SNN emulation time of less than 100 ms.