Refrigerant　injection　is　a　good　method　for　reducing　the　exhaust　temperature　of　a　single-screw　refrigeration　compressor　(SSRC).　In　this　paper,　an　accurate　method　is　proposed　to　calculate　the　variation　of　the　injection　area　for　different　initial　positions　and　different　sizes　of　injection　holes.　Furthermore,　a　mathematical　model　describing　the　internal　working　process　of　an　SSRC　with　liquid　refrigerant　injection　(LRI)　is　established　to　evaluate　the　performance　of　an　SSRC　and　heat　pump　with　a　variety　of　injection　hole　geometries　and　working　conditions.　This　theoretical　model　is　verified　by　comparing　the　calculation　results　with　experimental　data.　The　results　show　that　LRI　can　markedly　reduce　the　exhaust　temperature　and　improve　the　performance　of　the　SSRC　and　heat　pump　to　some　extent.　The　injection-hole　radius　is　the　most　important　factor　affecting　the　performance　of　the　compressor　and　heat-pump　system.　The　variations　of　different　performance　parameters　of　the　SSRC　and　heat　pump　at　low　ambient　temperature　can　be　obtained.　This　work　provides　a　theoretical　method　for　optimizing　the　injection　process　in　SSRCs.　(C)　2020　Elsevier　Ltd.　All　rights　reserved.