By measuring the probability density statistical characteristics of the duration time of single molecules fluorescence at on-and off-states, the effect of oxygen concentration on electron transfer dynamic characteristic of single molecules is studied. In the oxygen-rich environment, the fluorescence blinking of single molecules is caused by the electron population of ionic state and presents a power-law distribution. In the oxygen-poor environment, the fluorescence blinking of single molecules mainly stems from the electron population of triplet state and presents an exponential truncated power-law distribution. In the oxygen-specific environment, two kinds of electron transfer processes show an apparent competition effect, where part fluorescence blinking of single molecules follows a power-law distribution while the other part follows an exponential truncated power-law distribution.