An Artificial Neural Network (ANN) is an abstract representation of the biological nervous system which has the ability to solve many complex problems. The interesting attributes it exhibits makes an ANN capable of “learning”. ANN learning is achieved by training the neural network using a training algorithm. Aside from choosing a training algorithm to train ANNs, the ANN structure can also be optimized by applying certain pruning techniques to reduce network complexity. The Cat Swarm Optimization (CSO) algorithm, a swarm intelligence-based optimization algorithm mimics the behavior of cats, is used as the training algorithm and the Optimal Brain Damage (OBD) method as the pruning algorithm. This study suggests an approach to ANN training through the simultaneous optimization of the connection weights and ANN structure. Experiments performed on benchmark datasets taken from the UCI machine learning repository show that the proposed CSONN-OBD is an effective tool for training neural networks.