For　the　presence　of　various　uncertainties　in　rigid-body　systems,　a　function　approximation　technique　(FAT)　based　immersion　and　invariance　(I&I)　adaptive　control　method　is　proposed　for　rigid　body　attitude　control　in　this　paper.　The　system　model＇s　uncertainty　terms　are　aggregated　into　external　disturbances　and　parameterised　using　a　set　of　weighted　selected　basis　functions,　the　weights　of　these　functions　are　estimated　using　the　immersion　and　invariance　method.　Based　on　the　proposed　method,　a　control　law　based　on　terminal　sliding　mode　is　designed,　the　effectiveness　of　the　proposed　method　is　verified　through　stability　analysis.　Finally,　the　feasibility　of　the　method　is　demonstrated　through　simulations　of　rigid　body　attitude　under　various　uncertainties,　and　it　can　be　effectively　applied　in　the　attitude　control　of　rigid　body　such　as　vehicles,　spacecraft　and　robotic　arms.