Deep　learning　has　recently　garnered　significant　interest　in　many　applications　especially　for　big　data　analytics　in　the　edge　computing　environment.　Federated　learning,　as　a　novel　machine　learning　technique,　aims　to　build　a　shared　learning　model　from　training　data　on　distributed　edge　nodes　to　protect　data　privacy.　However,　the　model　update　in　federated　learning　requires　parameter　exchanges　among　edge　nodes,　which　is　rather　bandwidth-consuming.　This　article　proposes　a　novel　distributed　hierarchical　tensor　deep　computation　model　by　condensing　the　model　parameters　from　a　high-dimensional　tensor　space　into　a　set　of　low-dimensional　subspaces　to　reduce　the　bandwidth　consumption　and　storage　requirement　for　federated　learning.　Moreover,　an　updating　approach　with　a　hierarchical　tensor　back-propagation　algorithm　is　developed　by　directly　computing　the　gradients　of　low-dimensional　parameters　to　reduce　the　memory　requirement　of　training　for　edge　nodes　and　improve　training　efficiency.　Finally,　extensive　simulations　on　classical　datasets　with　different　local　data　distributions　are　presented　for　the　performance　evaluation.　The　results　demonstrate　that　the　proposed　model　relieves　the　burden　of　communication　bandwidth　and　reduces　energy　consumption　at　edge　nodes　for　federated　learning.