We　establish　the　improved　uniform　error　bound　on　the　time-splitting　Fourier　pseudospectral　(TSFP)　method　for　the　long-time　dynamics　of　the　generalized　fractional　nonlinear　Schrödinger　equation　(FNLSE)　with　O(ε2)-nonlinearity,　where　ε∈(0,1)　is　a　dimensionless　parameter.　Numerically,　we　discretize　the　FNLSE　by　the　second-order　Strang　splitting　method　in　time　and　Fourier　pseudospectral　method　in　space.　Combining　with　energy　method,　we　utilize　the　regularity　compensation　oscillation　(RCO)　technique　to　rigorously　prove　the　improved　uniform　error　bound　at　O(hm0　+ε2τ2)　with　the　mesh　size　h　and　time　step　τ　up　to　the　long-time　at　O(1/ε2),　which　gains　an　additional　ε2　in　time　compared　with　classical　error　estimates.　The　key　idea　behind　the　RCO　technique　is　to　analyze　low　frequency　modes　by　phase　cancellation　and　control　high　frequency　modes　by　the　regularity　of　the　exact　solution.　With　the　help　of　the　RCO　technique,　we　relax　some　constraints　in　the　previous　proof　for　the　improved　uniform　error　bound　and　extend　the　result　to　more　general　cases.　Finally,　numerical　examples　are　provided　to　confirm　our　improved　uniform　error　bound　and　demonstrate　its　suitability　in　different　cases.　©　2024　International　Press