By using datasets of HadISST monthly SST from 1895 to 2014 and 600-year simulations of two CESM model experiments with/without doubling of CO_2 concentration, ENSO characteristics (such as intensity, maximum signal location, lifetime and frequency) are compared pre- and post- global warming. The analysis periods are defined by the eras of 1895-1954 and 1955-2014 in the observations and the two model experiments, without and with doubling of CO_2 concentration, in the model, respectively. The main conclusions are as follows. Due to global warming, the maximum climatological SST warming occurs in the tropical western Pacific (La Nina-like background warming) and the tropical eastern Pacific (El Nino-like background warming) for observations and model, respectively, resulting in opposite zonal SST gradient anomalies in the tropical Pacific. The La Nina-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 Nino-like background warming causes westerly winds in the whole tropical Pacific and moves the strongest ocean-atmosphere coupling eastward. Different background warmings determine the different evolution characteristics of ENSO events. Under the background of La Nina-like 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 Nino-like background warming. ENSO lifetime is significantly extended under both the El Nino-like and the La Nina-like background warmings, and especially, it can be prolonged by up to 3 months in the situation of El Nino-like background warming. The prolonged El Nino lifetime mainly applies to extreme El Nino events, which is caused by two processes in response to global warming. On the one hand, the earlier outbreak of the westerly wind bursts (WWB) in the tropical western Pacific makes El Nino occur earlier. On the other hand, the climatological thermocline depth becomes shallower in the tropical Pacific, which can slow down the eastward propagation speed of the negative-feedback Kelvin wave in the subsurface ocean. In addition, the climatological upper-ocean temperature gradient between the equator and off-equator reduces in the tropical central-eastern Pacific, which can weaken the discharge rate of the ENSO warm signal. Both of the above processes make El Nino decay slowly and persist longer. 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 Nino and La Nina events appear under the El Nino-like and the La Nina-like background warmings, respectively. Based on the theories of ENSO evolution, this study shows the possible changes of ENSO characteristics in response to global warming, and reconciles the phenomena and mechanisms of different characteristics of ENSO changes in observations and models, which are essential for the understanding and prediction of the change of ENSO characteristics and its impact under the global warming background in the future.