In　the　current　application　of　robots,　the　robot　system　is　required　to　have　a　high　adaptability　to　unstructured　environment.　In　this　paper,　a　hexapod　robot　with　eccentric　wheels　was　studied,　and　its　basic　mechanical　structure　was　introduced.　The　motion　model　and　mechanical　constraints　of　the　hexapod　robot　when　climbing　a　slope　were　established　based　on　the　stable　cone　method.　A　wave-like　climbing　gait　was　designed.　The　most　easily　overturning　posture　of　the　robot　in　this　motion　mode　was　analyzed.　Combining　with　its　mechanical　structure　characteristics,　the　stability　of　the　robot　was　verified　by　using　the　stable　cone　method.　The　critical　slope　angle　of　the　robot　during　climbing　was　obtained　and　verified　by　simulation　and　physical　experiments.　In　this　mechanical　structure　and　the　use　of　the　corresponding　climbing　gait,　the　robot　can　have　better　climbing　performance.　The　maximum　stable　climbing　angle　of　the　robot　can　be　measured　in　the　experimental　environment　to　be　about　33　degrees.　©　2020,　Editorial　Department　of　Transaction　of　Beijing　Institute　of　Technology.　All　right　reserved.