The　vapor-injection　(VI)　technique　is　known　effective　for　improving　the　performance　of　air-source　heat　pump　(ASHP)　in　cold　climates.　Optimizing　the　intermediate　pressure　is　critical　for　the　efficiency　of　VI-ASHP　under　varying　operating　conditions,　while　model　based　control　is　cost　prohibitive　in　practice.　We　propose　an　extremum　seeking　control　(ESC)　framework　as　a　model-free　optimal　control　strategy　for　internal　heat　exchanger　(IHXC)　based　VI-ASHP,　minimizing　the　total　power　consumption　in　real　time.　The　ESC　takes　the　total　power　as　the　only　feedback,　and　the　intermediate　pressure　setpoint　as　the　manipulated　input.　A　Modelica-based　dynamic　simulation　model　of　an　IHXC-VI　ASHP　water　heater　is　developed.　The　water　outlet　temperature　is　regulated　by　the　compressor　capacity,　while　the　injection-loop　expansion　valve　regulates　the　intermediate　pressure.　Under　fixed,　staircase　and　realistic　ambient　temperature　profiles,　simulation　results　show　that　ESC　can　optimize　the　intermediate　pressure　for　system　efficiency　with　good　steady-state　and　transient　performance.　(C)　2019　Elsevier　Ltd　and　IIR.　All　rights　reserved.