Gigabyte H61 is a chipset not a motherboard model. The model would look like GA-H61M-S2PV, GA-H61M-USB3-B3, GA-H61-S3, etc. But looking at a few different GA-H61 models, they all seem to have a PCIe x16 slot so as long as your board has that port you'll have no issue putting the card in your motherboard.