I don't know where you got that 20amp figure. 20A times 12volts would be 240watts. An HD7770 does not use 240watts even when flat out - it's more like 80watts flat out.
I think that power supply will work just fine. It looks like - it's hard to read - that it has two 12volt "rails". If possible, when you connect the power to the HD7770, try to use both rails. This isn't always possible, depending upon the adapter you use and the layout of the cables. Some adapters have two Molex connectors for this reason. If it does, connect the Molex connectors to two different strings of connectors.
(Usually, you'll have cables (strings) coming from the power supply (PSU) that have 2 or 3 molex connectors on them, and often there will be more than one of these cables. Don't plug both molex connectors on the adapter into the same PSU cable - rather, spread them between two cables if possible. If you don't have 2 separate molex connectors on the adapter, or only one string from the PSU, don't worry about it. Or conversely, if the adapter has only one molex connector, connect it to a PSU string with nothing else on it - connect all the drives (hard drive, DVD) to a different string. All this is in an effort to balance the load between the two "rails".)
Edited by Quaker, 13 December 2012 - 03:54 PM.