In　this　paper,　we　use　genetic　algorithm　solve　problem　of　the　optimal　nonholonomic　motion　planning　of　free-floating　space　robot　system　with　dual-arms.　Base　on　the　linear　momentum　conservation.　and　the　angular　momentum　conservation　of　the　system,　the　system　state　equations　for　control　design　are　established.　The　approximate　optimal　control　scheme　of　the　system　proposed　is　studied,　and　a　genetic　algorithm　for　the　optimal　control　of　the　system　proposed　is　developed.　The　optimal　motion　planning　approach　proposed　possesses　the　advantages　that　it　can　obtain　the　desired　angles　of　the　base＇s　attitude　and　arms＇　joints　only　by　controlling　the　arms＇　joints　motion.　Some　simulations　for　a　planar　free-floating　space　robot　system　with　dual-arms　is　done　to　verified　the　proposed　approach.