A　protocol　is　proposed　for　the　preparation　of　high-fidelity　entangled　cat　states　with　composite　pulses.　The　physical　model　contains　two　Kerr-nonlinear　resonators　and　a　cavity.　By　properly　designing　the　parameters,　each　Kerr-nonlinear　resonator　is　confined　in　the　cat-state　subspace　and　the　entangled　cat　states　can　be　generated　efficiently.　Composite　two-photon　drives　are　introduced　with　multiple　amplitudes　and　frequencies　to　improve　the　fidelity　of　the　entangled　cat　states　in　the　presence　of　parameter　errors.　The　performance　of　the　protocol　is　estimated　by　taking　into　account　the　parametric　errors　and　decoherence.　Numerical　simulation　results　show　that,　the　protocol　is　robustness　to　timing　error,　detuning　error,　and　decoherence.　It　is　hoped　that　the　protocol　may　provide　a　method　for　preparing　stable　entangled　cat　states.