We　introduce　a　variable　selection　procedure　for　function-on-function　linear　models　with　multiple　functional　predictors,　using　the　functional　principal　component　analysis　(FPCA)-based　estimation　method　with　the　group　smoothly　clipped　absolute　deviation　regularization.　This　approach　enables　us　to　select　significant　functional　predictors　and　estimate　the　bivariate　functional　coefficients　simultaneously.　A　data-driven　procedure　is　provided　for　choosing　the　tuning　parameters　of　the　proposed　method　to　achieve　high　efficiency.　We　construct　FPCA-based　estimators　for　the　bivariate　functional　coefficients　using　the　proposed　regularization　method.　Under　some　mild　conditions,　we　establish　the　estimation　and　selection　consistencies　of　the　proposed　procedure.　Simulation　studies　are　carried　out　to　illustrate　the　finite-sample　performance　of　the　proposed　method.　The　results　show　that　our　method　is　highly　effective　in　identifying　the　relevant　functional　predictors　and　in　estimating　the　bivariate　functional　coefficients.　Furthermore,　the　proposed　method　is　demonstrated　in　a　real-data　example　by　investigating　the　association　between　ocean　temperature　and　several　water　variables.