In　this　paper,　a　fractional　order　sliding-mode　controller　with　predefined　tracking　time　is　proposed　for　servo　motor　to　achieve　trajectory　tracking.　The　proposed　controller　enables　the　angular　position　of　servo　motor　to　track　a　given　trajectory　at　a　tracking　time　tf　in　spite　of　disturbances/uncertainties,　and　the　tracking　time　can　be　set　in　advance.　The　proposed　controller　is　composed　of　two　parts:　the　first　one,　named　nominal　control,　is　based　on　optimal　control　theory　to　assure　the　states　of　disturbances　free　system　converge　to　zero　at　the　predefined　time.　The　second　part,　named　robust　control,　is　based　on　the　super-twisting　control　algorithm　(STA)　modified　with　the　fractional-order　integration,　allowing　the　integral　of　the　discontinuous　function　to　assume　a　fractional　order　to　compensate　the　disturbances　which　are　not　necessarily　integer-order　differentiable,　such　as　those　generated　from　dynamic　friction,　input　noise　and　mechanical　vibrations.　The　effectiveness　of　the　proposed　controller　is　demonstrated　on　a　DC　servo　system　via　simulation　and　experiments.　©　2022　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.