The　Strength　Pareto　Evolutionary　Algorithm　(SPEA)　is　adopted　to　find　time-jerk　synthetic　optimal　trajectory　of　a　hexapod　robot　in　the　joint　space.　In　order　to　get　the　optimal　trajectory,　cubic　splines　are　employed　and　derived　under　the　constraint　condition　of　via　points　to　assure　overall　continuity　of　velocity　and　acceleration.　Taken　both　the　execution　time　and　minimax　approach　of　jerk　as　objectives,　and　expressed　the　kinematics　constraints　as　upper　bounds　on　the　absolute　values　of　velocity　and　acceleration,　the　mathematic　model　of　time-jerk　synthetic　optimal　trajectory　planning　is　built.　Finally,　SPEA　is　adopted　to　optimize　the　stair-climbing　trajectory　of　a　hexapod　robot,　the　simulation　results　show　that　this　method　can　solve　the　trajectory　planning　problem　effectively,　and　the　stair-climbing　trajectory　can　meet　the　contradictory　objective　functions　of　high　speed　and　low　robot　vibration　well.