In　this　paper,　we　propose　a　protocol　to　realize　nonadiabatic　geometric　quantum　computation　(NGQC)of　W-state　codes　in　a　spin　system　using　invariant-based　reverse　engineering.　The　Heisenberg　XY　interaction　of　spin　qubits　provides　a　two-dimensional　computational　subspace　spanned　by　a　pair　of　W　states.　By　applying　a　time-dependent　magnetic　on　the　spin　qubits,　we　realize　the　effective　Pauli　operations　for　the　computational　subspace.　Assisted　by　the　invariant-based　reverse　engineering,　the　waveform　of　the　control　field　is　designed　and　the　evolution　paths　for　the　NGQC　is　found.　The　performance　of　the　protocol　under　the　influence　of　experimental　imperfections　is　estimated　by　the　numerical　simulations　with　available　parameters.　The　results　demonstrate　that　the　protocol　is　robust　against　systematic　error,　random　noise　and　decoherence.　Therefore,　the　protocol　may　be　promising　to　implement　fast　and　robust　manipulation　of　W　states　in　spin　systems.