This　paper　presents　an　efficient　suboptimal　model　predictive　control　(MPC)　algorithm　for　nonlinear　switched　systems　subject　to　minimum　dwell　time　constraints　(MTC).　While　MTC　are　required　for　most　physical　systems　due　to　stability,　power　and　mechanical　restrictions,　MPC　optimization　problems　with　MTC　are　challenging　to　solve.　To　efficiently　solve　such　problems,　the　on-line　MPC　optimization　problem　is　decomposed　into　a　sequence　of　simpler　problems,　which　include　two　nonlinear　programs　(NLP)　and　a　rounding　step,　as　typically　done　in　mixed-integer　optimal　control　(MIOC).　Unlike　the　classical　approach　that　embeds　MTC　in　a　mixed-integer　linear　program　(MILP)　with　combinatorial　constraints　in　the　rounding　step,　our　proposal　is　to　embed　the　MTC　in　one　of　the　NLPs　using　move　blocking.　Such　a　formulation　can　speedup　on-line　computations　by　employing　recent　move　blocking　algorithms　for　NLP　problems　and　by　using　a　simple　sum-up-rounding　(SUR)　method　for　the　rounding　step.　An　explicit　upper　bound　of　the　integer　approximation　error　for　the　rounding　step　is　given.　In　addition,　a　combined　shrinking　and　receding　horizon　strategy　is　developed　to　satisfy　closed-loop　MTC.　Recursive　feasibility　is　proven　using　a　l-step　control　invariant　(l-CI)　set,　where　l　is　the　minimum　dwell　time　step　length.　An　algorithm　to　compute　l-CI　sets　for　switched　linear　systems　off-line　is　also　presented.　Numerical　studies　show　significant　speed-up　and　comparable　control　performance　of　the　proposed　MPC　algorithm　against　the　classical　approach,　though　at　the　cost　of　significant　solution　quality　degradation　especially　when　the　MTC　are　large.(C)　2022　Elsevier　Ltd.　All　rights　reserved.