My friend put wild color card. It was my turn to put. Is it possible to put another wild color card?
According to this website, the rules for Wild cards state (emphasis mine):
This card represents all four colors, and can be placed on any card. The player has to state which color it will represent for the next player. It can be played regardless of whether another card is available.
So yes, a player may place a Wild on the pile in response to a Wild. However, if the card is a Wild +4, that player must have no cards of the color declared by the previous player, and may be challenged.