In　this　paper,　a　quantized　control　problem　is　investigated　for　a　class　of　networked　switched　systems　under　the　Round-Robin　protocol.　A　more　general　switching　rule　is　employed,　under　which　the　probability　distribution　of　switching　is　dependent　on　both　the　sojourn　time　and　the　system　mode.　The　Round-Robin　protocol　is　adopted　to　accommodate　the　limitation　of　the　network　bandwidth　from　the　viewpoint　of　fairness.　The　quantized　measurement　signal　is　sent　to　the　controller　as　a　feedback　signal　at　each　sampling　instant.　The　aim　of　the　problem　addressed　is　to　design　a　quantized　controller　such　that,　under　the　Round-Robin　protocol,　the　switched　system　with　the　known　joint　distribution　is　mean-square　stable.　Considering　the　sojourn　time　and　the　periodicity　of　Round-Robin　protocol,　we　present　an　interval-dependent　periodic　condition　to　guarantee　the　stability　of　addressed　systems　and　then　derive　the　explicit　expressions　of　the　controller　for　each　subsystem　by　solving　a　set　of　matrix　inequalities.　Finally,　a　simulation　example　is　given　to　demonstrate　the　effectiveness　of　the　controller　design　method.