Machine learning and complex network theory have emerged as crucial tools to extract meaningful information from big data, especially those related to complex systems. In this work, we aim to combine them to analyze El Niño Southern Oscillation (ENSO) phases. This non-linear phenomenon consists of anomalous (de)increase of temperature at the tropical Pacific Ocean, which has irregular occurrence and causes climatic variability worldwide. We construct temporal Climate Networks from the Surface Air Temperature time-series and calculate network metrics to characterize the warm and cold ENSO episodes. The metrics are used as topological features for classification. We employ ten classifiers and achieved 80% AUC ROC when predicting the intensity of Strong/ Weak El Niño and Strong/ Weak La Niña for the next season. The complex network represents the relationship among different regions of the planet and machine learning creates models to classify the different classes of ENSO. This work opens new paths of research by integrating network science and machine learning to analyze complex data like global climate systems.