No your PSU cannot handle it,
Buy yourself a decent one example:
http://uk.pcpartpicker.com/part/xfx-power-supply-p1450sx2b9
Have 12V 34A = 408W
Your curent PSU is simply junk quality:
"Avoid IMMEDIATELY. These units are highly unsafe to use. No such protections added, very thin gauge wiring used, false advertising and too much to list. Reference to a higher tiered unit for a better, money saving and a much safer unit. For your safety's sake, please don't order or pick one up for use in your system. These units are a potential fire hazard and could even kill you, let alone your system."
Source: http://www.tomshardware.co.uk/forum/id-2547993/psu-tier-list.html