The El Niño Southern Oscillation (ENSO) is one of the most powerful climate phenomena that can change global air circulation, affecting temperature and rainfall around the planet. ENSO has three phases: El Niño and La Niña are two extreme phases of the ENSO cycle, and ENSO neutral is a transitional period between El Niño and La Niña. Topological data analysis (TDA) is an innovative approach which focuses on a data set's "shape" or topological structures such loops, holes, and voids. We used TDA to describe the homology groups of the two-dimensional function determined by sea surface temperatures of tropical Pacific Ocean. The persistent homology of the function, which is determined by the monthly mean sea surface temperature in an expressed area of the Pacific, was used to identify ENSO phases. We classify using TDA summaries and compare the results to the existing NOAA classification utilizing topology information of sea surface temperatures of correctly specified ENSO phases. We compute the morse filtration's persistent homology for each month, then utilize the ECC to summarize the persistent homology. To reduce arbitrary errors and make the curve continuous, we utilized the smoothing function. We used LDA algorithm as a classification method and for dimension reduction, we used PCA transformation.