Hafnium　disulfide　(HfS2)　has　attracted　significant　interest　because　of　the　predicted　excellent　electronic　properties　superior　to　group　VIB　transition　metal　dichalcogenides.　On　the　other　hand,　atomically　thin　hexagonal　boron　nitride　(h-BN)　is　an　ideal　dielectric　substrate　for　optoelectronic　applications　of　other　2D　materials.　Here,　for　the　first　time,　we　report　the　direct　growth　of　high-quality　atomic　layered　HfS(2)on　few-layer　h-BN　transferred　on　SiO2/Si　substrates　by　chemical　vapor　deposition.　It　was　found　that　the　HfS(2)layers　are　selectively　grown　on　h-BN　rather　than　on　SiO2/Si.　Density　functional　theory　calculations　are　performed　to　help　understand　the　mechanism　of　selective　growth　of　HfS2.　Furthermore,　the　photodetectors　based　on　the　HfS2/h-BN　heterostructures　exhibit　excellent　visible-light　sensing　performance,　such　as　a　high　on/off　ratio　of　more　than　10(5),　an　ultrafast　response　rate　of　about　200　mu　s,　a　high　responsivity　of　26.5　mA　W-1,　and　a　competitive　detectivity　exceeding　3　x　10(11)Jones,　superior　to　the　vast　majority　of　the　reported　2D　materials　based　photodetectors.　The　remarkable　performance　of　the　HfS2/h-BN　photodetector　is　attributed　to　the　unique　features　of　2D　h-BN　substrate.