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The real-time prediction skill for El Nino-Southern Oscillation has not improved steadily during the twenty-first century. One important reason is the season-dependent predictability barrier (PB), and another is due to the diversity of El Nino. In this paper, an approach to data analysis for predictability is developed to investigate the season-dependent PB phenomena of two types of El Nino events by using the monthly mean data of the preindustrial control ("pi-Control") runs from several coupled model outputs in CMIP5 experiments. The results find that predictions for Central Pacific El Nino (CP-El Nino) suffered from summer PB, whereas those for Eastern Pacific El Nino (EP-El Nino) are mainly interfered with by spring PB. The initial errors most frequently causing PB for CP- and EP-El Nino are revealed and they emphasize that the initial sea temperature accuracy in the Victoria mode (VM) region in the North Pacific is more important for better predictions of the intensity of the CP-El Nino, whereas that in the subsurface layer of the west equatorial Pacific and the surface layer of the southeast Pacific is of more concern for better predictions of the structure of CP-El Nino. However, for EP-El Nino, the former is indicated to modulate the structure of the event, whereas the latter is shown to be more effective in predictions of the intensity of the event. Obviously, for predicting which type of El Nino will occur, more attention should be paid to the initial sea temperature accuracy in not only the subsurface layer of the west equatorial Pacific and the surface layer of the southeast Pacific but also the region covered by the VM-like mode in the North Pacific. This result provided guidance aiming at how to initialize model in predictions of El Nino types.