A　scheme　is　proposed　to　deterministically　generate　four-dimensional　entangled　states　for　two　distant　atoms　trapped　in　two　separate　cavities　via　adiabatic　passage　by　one　step.　An　optimal　expression　of　time-dependent　Rabi　frequencies　is　selected　through　numerical　simulation.　Numerical　simulation　also　shows　that　the　excited　probabilities　of　the　atoms,　the　cavity　modes　and　the　fiber　modes　are　very　low　during　adiabatic　passage,　and　the　scheme　is　insensitive　to　the　fluctuation　of　experimental　parameters.　The　four-dimensional　entanglement　may　be　generated　with　high　fidelity　with　current　experimental　technology.　©　2012　The　Royal　Swedish　Academy　of　Sciences.