By using datasets of HadISST monthly SST from 1895 to 2014 and 600-year simulations of two CESM model experiments with/without doubling of CO2 concentration, ENSO characteristics are compared pre- and post- global warming. The main results are as follows. Due to global warming, the maximum climatological SST warming occurs in the tropical western Pacific (La Niña-like background warming) and the tropical eastern Pacific (El Niño-like background warming) for observations and model, respectively, resulting in opposite zonal SST gradient anomalies in the tropical Pacific. The La Niña-like background warming induces intense surface divergence in the tropical central Pacific, which enhances the easterly trade winds in the tropical central-western Pacific and shifts the strongest ocean-atmosphere coupling westward, correspondingly. On the contrary, the El Niño-like background warming causes westerly winds in the whole tropical Pacific and moves the strongest ocean-atmosphere coupling eastward. Under the La Niña-like background warming, ENSO tends to develop and mature in the tropical central Pacific, because the background easterly wind anomaly weakens the ENSO-induced westerly wind anomaly in the tropical western Pacific, leading to the so-called "Central Pacific ENSO (CP ENSO)". However, the so-called "Eastern Pacific ENSO (EP ENSO)" is likely formed due to increased westerly wind anomaly by the El Niño-like background warming. ENSO lifetime is significantly extended under both the El Niño-like and the La Niña-like background warmings, and especially, it can be prolonged by up to 3 months in the situation of El Niño-like background warming. The prolonged El Nino lifetime mainly applies to extreme El Niño events, which is caused by earlier outbreak of the westerly wind bursts, shallower climatological thermocline depth and weaker "discharge" rate of the ENSO warm signal in response to global warming. Results from both observations and the model also show that the frequency of ENSO events greatly increases due to global warming, and many more extreme El Niño and La Niña events appear under the El Niño-like and the La Niña-like background warmings, respectively. This study reconciles the phenomena and mechanisms of different characteristics of ENSO changes in observations and models.