Kamelox,
Welcome to the ROG forums, this may be a tough one to answer, looking at the specs on that site it says you have a 230 watt power supply.
Looking on ASUS site
http://www.asus.com/us/Desktops/ROG_G20AJ/specifications/ this model is available with up to a GTX 780, so a 970 or 980 may fit in the chassis, but looking at the available power supplies, it says a 180 + 230 watt, so just by reading the specs I would say you are limited by your power supply and may not be able to upgrade, or if you are I would only go to the GTX 970, not knowing the layout of your chassis you may also be limited to the size of the graphics card and may need one of the smaller size cards. It would be worth investigating obtaining the optional power supply'
http://www.pcmag.com/article2/0,2817,2470952,00.aspAnother unusual innovation is the two external power supply units that the G20 needs run. Asus did this to shrink the chassis, but the inconvenience of finding a free power plug is multiplied twice over as a result. Asus says it's more efficient to dedicate one of the power supplies to the discrete graphics card, but that also means that the system will take up at least three power plugs: one for the display and two for the PC.