As　a　fast　emerging　topic,　van　der　Waals　(vdW)　heterostructures　have　been　proposed　to　modify　two-dimensional　layered　materials　with　desired　properties,　thus　greatly　extending　the　applications　of　these　materials.　In　this　work,　the　stacking　characteristics,　electronic　structures,　band　edge　alignments,　charge　density　distributions　and　optical　properties　of　blue　phosphorene/transition　metal　dichalcogenides　(BlueP/TMDs)　vdW　heterostructures　were　systematically　studied　based　on　vdW　corrected　density　functional　theory.　Interestingly,　the　valence　band　maximum　and　conduction　band　minimum　are　located　in　different　parts　of　BlueP/MoSe2,　BlueP/WS2　and　BlueP/WSe2　heterostructures.　The　MoSe2,　WS2　or　WSe2　layer　can　be　used　as　the　electron　donor　and　the　BlueP　layer　can　be　used　as　the　electron　acceptor.　We　further　found　that　the　optical　properties　under　visible-light　irradiation　of　BlueP/TMDs　vdW　heterostructures　are　significantly　improved.　In　particular,　the　predicted　upper　limit　energy　conversion　efficiencies　of　BlueP/MoS2　and　BlueP/MoSe2　heterostructures　reach　as　large　as　1.16%　and　0.98%,　respectively,　suggesting　their　potential　applications　in　efficient　thin-film　solar　cells　and　optoelectronic　devices.