In　this　paper,　we　propose　a　protocol　to　realize　the　conversions　between　Greenberger-Horne-Zeilinger　(GHZ)　states　and　W　states　of　spin　qubits.　By　analyzing　and　simplifying　the　dynamics　of　the　system,　the　control　fields　are　designed　via　the　inverse　Hamiltonian　engineering　based　on　the　Lie　transforms.　Moreover,　the　states＇　conversions　between　multitype　GHZ　states　and　W　states　can　be　executed　deterministically　and　reversibly,　which　makes　the　protocol　resource　saving　and　flexible.　We　show　in　numerical　simulations　that　the　state　conversions　are　robust　against　the　systematic　errors,　random　noise,　and　frequency　mismatching　of　the　control　fields.　Therefore,　the　protocol　may　provide　some　useful　prospectives　to　the　research　of　quantum　mechanics　and　applications　of　quantum　information　processing　based　on　GHZ　states　and　W　states.　©　2019　American　Physical　Society.