If you have a 125W CPU, plus 230W for the GTX 770 and allowing 40W for other components, that is 395W total.
Most of this is on the +12V rails and we want to keep these under 80% load, so minimum required rating on the +12V rails is 42A.
Your supply has two rails, each rated at 22A, so if they are evenly balanced this should be OK.
As for quality, I can't find any detailed reviews for your supply.
The fact that irt is not 80 plus rated and the lack of reviews is not a good sign.
If you are at all concerned, consider any of the supplies below:
XFX Core 650 (XFX Pro 650)
Seasonic G 650
Seasonic S12G 650
Antec HCG 620 (Antec High Current Gamer 620)
Corsair TX 650
Corsair HX 650
Seasonic X 650