In　this　paper,　a　protocol　for　nondestructive　parity　meter　(NPM)　of　two　cat-state　qubits　is　proposed.　The　physical　model　contains　two　cavities　and　an　auxiliary　qubit.　For　each　cavity,　the　quantum　information　is　encoded　on　the　odd　and　even　cat　state,　forming　a　cat-state　qubit.　By　adjusting　the　strength　of　the　driving　field　on　the　auxiliary　qubit,　an　effective　Hamiltonian　for　cavity-selective　transition　is　derived.　Moreover,　reverse　engineering　based　on　the　effective　Hamiltonian　is　applied　to　find　the　evolution　path,　and　the　systematic-error-sensitivity　nullification　method　is　used　to　select　proper　parameters　of　the　evolution　path.　In　this　way,　robust　control　fields　are　designed　to　combat　the　influence　of　the　systematic　errors.　Furthermore,　the　effects　of　random　noise　and　decoherence　on　the　fidelity　of　the　protocol　are　considered.　Numerical　simulations　show　that　the　protocol　is　insensitive　to　the　experimental　imperfection,　including　systematic　errors,　random　noise　and　decoherence.　Therefore,　the　protocol　is　expected　to　expand　the　vision　of　realizing　NPM.