The 31-year-old admitted posting a comment on his Twitter account which was abusive and/or insulting and/or improper and/or brought the game into disrepute, in breach of FA Rule E3.
The charge related to Cole’s involvement in a Twitter altercation with a Tottenham fan following West Ham’s 2-2 draw in their Premier League game at White Hart Lane on February 22.
Cole, who was also fined ??20,000 by the FA in 2011 for an identical offence, has made 17 appearances for the Hammers in all competitions this season, scoring three goals.
However, he is currently on the sidelines after suffering a hamstring during the game against Spurs.