As　an　attractive　catalyst　for　the　electrochemical　hydrogen　evolution　reaction(HER),　MoTe2　has　attracted　great　interest.　However,　scarce　catalytic　sites　and　unsatisfactory　catalytic　activity　of　pristine　MoTe2　basal　plane　impeded　its　practical　application.　The　incorporation　of　single　metal　atom　into　2D-substrate　have　been　demonstrated　as　an　effective　strategy　to　tune　HER　activity　of　materials.　Herein,　we　systematically　investigated　a　series　of　transition-metal　atoms(Fe,　Co,　Ni,　Cu,　Ru,　Rh,　Pd　and　Ag)　embedded　MoTe2　plane　and　edge　single-atom　catalysts(SAC,　TM-MoTe2)　for　HER　performance　by　employing　density　functional　theory　calculations.　All　TM-MoTe2　catalysts　exhibit　good　thermodynamically　and　electrochemical　stability.　Compared　with　pristine　MoTe2,　HER　catalytic　activity　of　TM-MoTe2　are　significantly　enhanced　due　to　effective　modulation　of　charge　transfer　on　embedded　metal,　which　attribute　to　synergy　interaction　between　embedded　TM　and　surrounding　Mo　atoms.　Specially,　2　candidate　catalysts　with　Ru-MoTe2　plane　and　Fe-MoTe2　edge　are　found　to　show　higher　HER　catalytic　performance　with　low　overpotential　of　only　10　mV　and　60　mV,　respectively.　Furthermore,　we　found　a　key　descriptor　Δdd′　to　well　predict　HER-activity　trend　of　MoTe2-based　material,　which　is　closely　correlated　with　H　adsorption　energy(ΔEH).　This　work　provides　in-depth　theoretical　insights　for　understanding　active　sites　and　designing　high-efficiency　MoTe2-based　HER　catalysts.　©　2024　Elsevier　B.V.