This　paper　investigates　the　problem　of　error　reachable　set　estimation　for　leader-follower　systems　under　semi-Markov　switching　topology　with　partially　unknown　rates.　The　topology　switching　is　controlled　by　a　semi-Markov　jump　process.　It　is　difficult　to　find　the　transition　rates　matrix　completely　in　many　practical　systems　so　that　we　come　to　a　conclusion　that　the　transition　rates　is　incompletely　known.　In　this　paper,　we　take　the　external　perturbation　problem　and　nonlinearity　into　account.　By　using　the　stochastic　theory　and　the　reachable　set　theory,　we　derive　the　sufficient　conditions　for　the　use　of　linear　matrix　inequalities　to　ensure　that　the　error　trajectory　can　be　constrained　in　a　given　closed　space　under　a　given　performance　index.　Finally,　an　example　is　given　to　verify　the　effectiveness　of　the　theoretical　results　©　2021　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.