In　this　paper,　a　flexible　and　effective　scheme　is　proposed　to　realize　nonadiabatic　geometric　quantum　gates　with　the　invariant　based　reverse　engineering　and　the　nonadiabatic　holonomic　quantum　computation　(NHQC+)　presented　in　recent　work　[B.-J.　Liu　et　al.,　Phys.　Rev.　Lett.　123,　100501　(2019)PRLTAO0031-900710.1103/PhysRevLett.123.100501]　for　extensible　geometric　quantum　computation.　The　scheme　provides　variabilities　for　most　of　control　parameters,　and　can　build　up　multiple　evolution　paths　with　different　geometric　phases　acquired　in　a　cycling　evolution.　As　the　computational　basis　can　be　covered　by　the　evolution　paths,　the　realization　of　the　nonadiabatic　geometric　quantum　computation　is　possible　without　auxiliary　levels.　Moreover,　multiple　types　of　nonadiabatic　geometric　quantum　gates　can　also　be　easily　constructed　by　only　adjusting　boundary　conditions　of　control　parameters　with　the　method.　To　show　the　applications　of　the　scheme,　we　discuss　the　implementations　of　nonadiabatic　geometric　quantum　gates　of　spin　qubits　in　a　double-quantum-dot　system　with　numerical　simulations.　The　results　indicate　that　the　scheme　possesses　robustness　against　the　errors　and　noise.　Therefore,　the　scheme　may　offer　some　interesting　perspectives　for　the　realization　of　the　nonadiabatic　geometric　quantum　computation.　©　2020　American　Physical　Society.