Horizons in a seismic image are geologically signficant surfaces that can be used for understanding geological structures and stratigraphy models. However, horizon tracking in seismic data is a time consuming and challenging task. Saving geologist's time from this seismic interpretation task is essential given the time constraints for the decision making in the oil & gas industry. We take advantage of the deep convolutional neural networks (CNN) to track the horizons directly from the seismic images. We propose a novel automatic seismic horizon tracking method that can reduce the time needed for interpretation, as well as increase the accuracy for the geologists. We show the performance comparison of the proposed CNN model for different training data set sizes and different methods of balancing the classes.