I think that your cube has been put together incorrectly at some point. If you take a solved cube and try to put it in the state of the cube in that picture, you won't be able to do it. On the 3x3x3 Rubik's cube, you can't have just one edge piece unsolved. You will have to get the puzzle back to normal to solve it.
To do this, you need take out the edge piece and put it back in so that you have the yellow cross. Turn a layer with the edge in it 45 degrees and then take the edge out. You can see how to do this in the beginning of this video
. Once it's out, put it back in so that the yellow cross is made. You should be able to solve the puzzle now.