Considering　the　size　of　an　irreversible　air　heat　pump　(AHP),　heating　load　density　(HLD)　is　taken　as　thermodynamic　optimization　objective　by　using　finite-time　thermodynamics.　Based　on　an　irreversible　AHP　with　infinite　reservoir　thermal-capacitance　rate　model,　the　expression　of　HLD　of　AHP　is　put　forward.　The　HLD　optimization　processes　are　studied　analytically　and　numerically,　which　consist　of　two　aspects:　(1)　to　choose　pressure　ratio;　(2)　to　distribute　heat-exchanger　inventory.　Heat　reservoir　temperatures,　heat　transfer　performance　of　heat　exchangers　as　well　as　irreversibility　during　compression　and　expansion　processes　are　important　factors　influencing　on　the　performance　of　an　irreversible　AHP,　which　are　characterized　with　temperature　ratio,　heat　exchanger　inventory　as　well　as　isentropic　efficiencies,　respectively.　Those　impacts　of　parameters　on　the　maximum　HLD　are　thoroughly　studied.　The　research　results　show　that　HLD　optimization　can　make　the　size　of　the　AHP　system　smaller　and　improve　the　compactness　of　system.