A　self-balancing　unicycle　robot,　which　consists　of　a　wheel　for　balancing　and　movement　in　longitudinal　(pitch)　as　well　as　a　flywheel　for　balancing　in　lateral　(roll),　is　studied　in　this　paper.　The　Lagrange　approach　is　used　to　formulate　the　dynamic　model,　and　the　control　algorithm　of　the　self-balancing　unicycle　robot　is　presented.　Because　of　the　structure　feature,　there　is　no　direct　force　to　change　yaw　direction　of　the　unicycle　robot,　only　can　we　achieve　it　by　using　the　interaction　between　individual　motions　in　the　yaw,　pitch　and　roll　direction.　Simulation　results　validates　that　the　unicycle　robot　can　both　change　the　yaw　direction　and　keep　its　posture　stable.