Quantum　holonomic　gates　hold　built-in　resilience　to　local　noises　and　provide　a　promising　approach　for　implementing　fault-tolerant　quantum　computation.　We　propose　to　realize　high-fidelity　holonomic　(N+1)-qubit　controlled　gates　using　Rydberg　atoms　confined　in　optical　arrays　or　superconducting　circuits.　We　identify　the　scheme,　deduce　the　effective　multibody　Hamiltonian,　and　determine　the　working　condition　of　the　multiqubit　gate.　Uniquely,　the　multiqubit　gate　is　immune　to　systematic　errors,　i.e.,　laser　parameter　fluctuations　and　motional　dephasing,　as　the　N　control　atoms　largely　remain　in　the　very　stable　qubit　space　during　the　operation.　We　show　that　CN-not　gates　can　reach　the　same　level　of　fidelity　at　a　given　gate　time　for　N≤5　under　a　suitable　choice　of　parameters,　and　the　gate　tolerance　against　errors　in　systematic　parameters　can　be　further　enhanced　through　optimal　pulse　engineering.　In　the　case　of　Rydberg　atoms,　the　proposed　protocol　is　intrinsically　different　from　typical　schemes　based　on　Rydberg　blockade　or　antiblockade.　Our　study　paves　an　alternative　way　to　build　robust　multiqubit　gates　with　Rydberg　atoms　trapped　in　optical　arrays　or　with　superconducting　circuits.　It　contributes　to　current　efforts　to　develop　scalable　quantum　computation　with　trapped　atoms　and　fabricable　superconducting　devices.　©　2021　American　Physical　Society.