The　unconventional　photon　blockade,　which　relies　on　the　physical　mechanism　of　quantum　interference,　is　primarily　investigated　using　a　general　master　equation,　where　a　weak　nonlinearity　must　be　presented　in　the　system　to　achieve　photon　antibunching.　In　this　study,　we　explore　the　unconventional　photon　blockade　using　an　alternative　master　equation　known　as　the　two-photon　absorption　master　equation,　which　is　derived　from　the　system　and　environment　interaction　via　two-photon　absorption.　Specifically,　we　find　that　the　unconventional　photon　blockade　can　be　triggered　in　two-coupled　cavities,　where　each　cavity　interacts　with　a　two-photon　absorption　environment.　Different　from　unconventional　photon　blockade　via　the　general　master　equation,　we　show　that　the　two-photon　absorption　acts　as　the　weak　nonlinearity,　and　this　photon　blockade　corresponds　to　a　large　average　photon　number.　To　derive　optimal　conditions　for　achieving　this　blockade,　we　propose　a　non-Hermitian　Hamiltonian　method　to　describe　the　mode　loss　caused　by　the　two-photon　absorption.　In　addition,　we　highlight　the　distinctions　between　our　proposal　and　other　approaches　for　generating　single-photon　states　based　on　two-photon　absorption.　©　2024　IOP　Publishing　Ltd.