Depending on some of the dimensions of your GPU, there can be problems with clearance within the H1 case. These dimensions are the following:
Dimensions - 305mm (L) x 128mm (W) OR 265mm (L) x 145mm (W)
Thickness/Depth - Up to 2.5 slots (50mm)
A GPU that does not fall within these requirements may still be able to fit, but this may require the air filter to be removed or for modifications to be made to the chassis. We would not recommend removing your air filter as dust buildup within your GPU can be difficult to clean. Additionally, any modifications to the NZXT H1 can void your warranty.