The Super Saiyan God Transformation
The SSJ God Transformation is a special transformation which is achieved when a pure-hearted saiyans receive the power of 5 others pure-hearted saiyans. The power given by this transformation is fantastic but it doesn't last very long, excepted for Goku who managed to absorb the God mode inside himself. This Super Saiyan God transformation is seen for the first time in the 2013 Dragon Ball Movie "Battle of the Gods" and it is availables in Dragon Ball games published after the film such as Battle of Gods, Dragon Ball Xenoverse or games which are constantly updated like Dragon Ball Heroes.
The movie "Battle of the Gods" is based on Akira Toriyama's new full color manga with the same name, so the Super Saiyan God transformation is a cannon transformation.
How looks like a Super Saiyan God
When he transformed into a Super Saiyan God, Goku still has base form hairs but they are red, his eyes are red and black, his skin color is brighter, his body thiner and a flame-like aura surround him.
Goku SSJ God as seen in the Battle of Gods movie and in Battle of Z
Promo picture from the official manga "Battle of Gods"
The manga "Battle of Gods" was published in Japan the 4th October 2013 by Akira Toriyama.