A　large　amount　of　calculation　is　needed　when　model　predictive　control　(MPC)　is　implemented　in　quasi-Z-source　inverter　(qZSI).　To　solve　this　problem,　an　improved　MPC　algorithm　is　applied　to　the　qZSI.　The　proposed　method　is　based　on　sector　distribution　and　new　voltage　vector　selection　method.　It　improves　the　quality　of　load　current　and　reduces　the　amount　of　calculation　greatly.　The　simulation　results　show　that　the　proposed　MPC　algorithm　has　excellent　dynamic　and　static　performance.　©　2019　IEEE.