From limited information you have provided, it would be hard to tell.
However, from the "...shall not exceed 320W..." we can tell that the PSU you have is only 320W, AT BEST. HD 7770 requires a 6-pin and is rated for around 80Watts. Even if it was a fairly low spec system, it may only be JUST enough to power that gpu. It would be best to buy something with that is in the range of 450-600Watts.
There are websites with online calculators that can help provide a rough estimate of the wattage of your system and also determine a reccomended wattage that your PSU should have.
http://outervision.com/power-supply-calculator