Thin-GaN light-emitting diodes were fabricated by Au-Si wafer bonding and laser lift-off. The relaxation process of the thermal strain in the transferred GaN films on a Si substrate was studied by varying the bonding film thickness of the Au over a wide range from 7 μm to 40 μm. The transferred GaN films were found to be strained by the biaxial compressive stress. A 10 μm Au bonding layer thickness was proven to have the lowest residual compressive stress, and the complete compressive stress variation throughout the entire thin-GaN fabrication process is discussed. Finally, we changed the biaxial in-plane stress of the transferred GaN thin film by controlling the bonding conditions, including the bonding layer thickness and the bonding temperature.