The　performance　optimisation　has　been　studied　for　an　endoreversible　air　heat　pump　with　variable　temperature　heat　reservoirs　by　taking　heating　load,　coefficient　of　performance　(COP)　and　heating　load　density,　i.e.　the　ratio　of　heating　load　to　the　maximum　specific　volume　in　the　cycle,　as　the　optimisation　objectives　in　this　paper.　The　analytical　relations　of　the　heating　load,　the　COP　and　heating　load　density　are　derived.　The　effects　of　pressure　ratio,　the　effectiveness　of　the　heat　exchangers　and　the　inlet　temperature　ratio　of　the　heat　reservoirs　on　the　heating　load,　the　COP　and　the　heating　load　density　are　analysed.　The　cycle　performance　optimisations　are　performed　by　searching　the　optimum　distribution　of　heat　conductance　of　the　hot　and　cold　side　heat　exchangers　for　fixed　total　heat　exchanger　inventory　and　the　optimum　heat　capacity　rate　matching　between　the　working　fluid　and　the　heat　reservoirs.　The　air　heat　pump　plant　design　with　heat　loading　density　optimisation　leads　to　a　smaller　size　including　the　compressor,　expansion　turbine,　and　the　hot　and　cold　side　heat　exchangers.