NVIDIA GigaByte GTX970 G1 GAMING would work with my psu?

Solution
Yeah, it has 2 6 pin +2 PCIe connections, so it will run the 970. But I would not use the PSU. There are a lot of really bad PSUs on the market and a malfunction can damage your hardware. I would look for a quality PSU from Seasonic, EVGA, or Corsair.