In this study, we investigate the outage performance of full-duplex fixed-gain amplify-and-forward (AF) relaying systems over Rayleigh fading channels. New exact outage probability expression of full-duplex fixed-gain AF relaying is derived analytically in single-integral form by using the cumulative distribution function (CDF) approach. The analytical results for outage performance are verified by Monte-Carlo type computer simulations. We observe that the error floor caused by loop-interference at the full-duplex fixed-gain relay occurs for larger values of the loop interference power. Furthermore, the results are compared with full-duplex variable-gain AF relaying results given in the literature. In addition to simpler structure advantage of fixed-gain relaying compared to variable-gain relaying, it is shown that full-duplex fixed-gain AF relaying provides better outage performance. Contrary to the full-duplex fixed-gain AF relaying, the error floor is observed for the full-duplex variable-gain AF relaying for even small values of the loop interference power.