Van　der　Waals　(vdW)　heterostructures　comprising　of　transition　metal　dichalcogenides　(TMDs)　and　hexagonal　boron　nitride　(h-BN)　are　promising　building　blocks　for　novel　2D　devices.　The　vdW　epitaxy　provides　a　straightforward　integration　method　for　fabricating　high-quality　TMDs/h-BN　vertical　heterostructures.　In　this　work,　the　vdW　epitaxy　of　high-quality　single-crystal　HfSe2　on　epitaxial　h-BN/sapphire　substrates　by　chemical　vapor　deposition　is　demonstrated.　The　epitaxial　HfSe2　layers　exhibit　a　uniform　and　atomically　sharp　interface　with　the　underlying　h-BN　template,　and　the　epitaxial　relationship　between　HfSe2　and　h-BN/sapphire　is　determined　to　HfSe2　(0001)[12${\mathrm{\bar{2}}}$10]//h-BN　(0001)[11${\mathrm{\bar{1}}}$00]//sapphire　(0001)[11${\mathrm{\bar{1}}}$00].　Impressively,　the　full　width　at　half　maximum　of　the　rocking　curve　for　the　epitaxial　HfSe2　layer　on　single-crystal　h-BN　is　as　narrow　as　9.6　arcmin,　indicating　an　extremely　high　degree　of　out-plane　orientation　and　high　crystallinity.　Benefitting　from　the　high　crystalline　quality　of　HfSe2　epilayers　and　the　weak　interfacial　scattering　of　HfSe2/h-BN,　the　photodetector　fabricated　from　the　vdW　epitaxial　HfSe2　on　single-crystal　h-BN　shows　the　best　performance　with　an　on/off　ratio　of　1　x　104　and　a　responsivity　up　to　43　mA　W-1.　Furthermore,　the　vdW　epitaxy　of　other　TMDs　such　as　HfS2,　ZrS2,　and　ZrSe2　is　also　experimentally　demonstrated　on　single-crystal　h-BN,　suggesting　the　broad　applicability　of　the　h-BN　template　for　the　vdW　epitaxy.　Several　high-quality　single-crystalline　transition　metal　dichalcogenides　are　directly　grown　on　an　epitaxial　h-BN/sapphire　substrate　via　vdW　epitaxy,　indicating　the　h-BN　is　an　ideal　template　for　vdW　epitaxy.　The　full　width　at　half　maximum　of　the　X-ray　diffraction　rocking　curve　for　the　HfSe2　layers　on　single-crystal　h-BN　is　only　9.6　arcmin,　indicating　an　extremely　high　degree　of　out-plane　orientation　and　high　crystallinity.　image