Neural network (NN) tools are suitable for many tasks such as classification, clustering, scheduling and prediction. NN performance depends on the strategy of learning a phenomenon, the number of hidden nodes, activation function and, of course, the behavior of the data. There are many techniques used for training NN, while the social insect's techniques become more focused by researchers because of its natural behavioral processing. The Artificial Bee Colony (ABC) algorithm has produced an easy way for solving combinatorial, statistical problems and for training NN by different organized agents. The objective of training NN is to adjust the weights so that application of a set of inputs produces the desired set of outputs. Normally, NN is trained by a standard backpropagation (BP) algorithm; however, BP is too slow for many applications and trapping in a local minima problem. To recover the above gap, the hybrid technique was used for training NN here. The hybrid of natural behavior agent ant and bee techniques was used for training NN. The simulation result of a Hybrid Ant Bee Colony (HABC) was compared with, ABC, BP Levenberg-Mardquart (LM) and BP Gradient Descent (GD) learning algorithms. According to experimental results, the proposed HABC algorithm did improve the classification accuracy for the Boolean function, and prediction of volcano time-series data, which was used to train the MLP.