Not sure - Writer doesn't say.
Two reasons - Selfish, wants to live own life.
Help Lennie/save Lennie
Why does George kill Lennie in the novel, Of Mice and Men?
There are various reasons that explain why George killed Lennie in the novel, but the author doesn't give a reason. Instead the author leaves this to reader's imagination. George could have been selfish and killed Lennie so he could live his own life. Maybe George feels like Lennie's parents. For example, when Lennie touched a woman's dress, they had to move out of the country and start life again. For this reason, perhaps George killed Lennie because he didn't want to take care of Lennie.
The other option of why George killed Lennie was that he could have been thinking of Lennie's punishment and about Lennie being hanged for the murder of Curley's wife. George could have stopped Lennie from the pain of being hanged by shooting Lennie in the back of the head just as Curley had done to Candy's dog.
Perhaps the reader can understand that 'George is being cruel to be kind'. For example, earlier in the novel, George threw away the dead rat and shouted at Lennie for Lennie's own good, but George did not show this in a nice way to Lennie.
Therefore we can conclude that George was either a bad person who could have killed Lennie for himself or he could have been saving his friend from a painful death.