Really need more info.
When You see 300 Watts required for a given GPU, that is (A) Not just the GPU, but the Whole system and (B) they are over rating to compensate for the "crappy" pSU that are on the market.
Without knowing your Graphics card, nor your computer (Really just the CPU and is it Overclocked) and the Brand/model of your PSU it is really hard to give a answer.
The comments about the quality of your PSU, may be spot on, But unk untill you identify.
An example: I have a I5-2500k OCed to 4.2 GHz) with a 6870 ATI GPU. The power measured at the wall is 350 W when fully loaded (ie running furmark). My I5-750 OCed to 3.2 GHz w/ATI 6770 GPU is around 300 Watts when running furmark.
What I do is google a review of the GPU card and look to see what their system power is. Then the Minium size that I would use whould be (a) AT least 30 % higher, ie min for 350 watt should be 450 Watt and for a 300 W say a 400 Watt. NOTE, I'm NOT USING THE wattage provided by GPU, nor calculators!!! And (B) make sure it is a quality PSU - google reviews for it!!.
Just Like I would not buy a Cheap, low quality, pron to fail pacesmaker for my heart, I would NOT recommend a PSU that is better used to prop a door open than to operate/protect all of the rest of my computer.