We　propose　a　low-complexity　semi-blind　joint　multi-　carrier　frequency　offset　(CFO)　and　multi-channel　estimation　scheme　for　uplink　generalized　frequency　division　multiple　access　(GFDMA)　systems.　To　the　best　of　our　knowledge,　this　is　the　first　work　to　investigate　the　estimation　of　both　CFOs　and　channels　for　a　wide　range　of　GFDMA　systems,　allowing　arbitrary　carrier　assignment,　modulation　type　and　cyclic　prefix　length,　and　a　wide　range　of　the　number　of　receive　antennas.　Thanks　to　the　orthogonality　between　noise　subspace　and　each　signal　subspace　of　U　users,　a　complex　U-CFO　and　U-channel　estimation　problem　is　decomposed　into　2U　one-dimensional　problems,　and　solved　in　a　semi-blind　manner.　Also,　the　multi-CFO　compensation　is　performed　at　receiver　rather　than　transmitter,　avoiding　spectral　overhead　due　to　feedback　of　multiple　CFOs.　Simulation　results　show　that　the　proposed　scheme　significantly　outperforms　the　existing　methods　in　terms　of　bit　error　rate　(BER)　and　root-mean-square-errors　(RMSEs)　of　CFO　and　channel　estimation,　at　much　lower　computational　complexity　than　the　existing　methods.　©　2019　IEEE.