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In this paper, we establish a singular Trudinger-Moser inequality for the whole hyperbolic space H^n: sup_u∈W^1,n(H^n),∫_H^n|∇_H^nu|^ndμ ≤ 1∫_H^ne^α|u|nn-1 -Σ^n-2_k=0α^k|u|^nkn-1 k! ρ^βdμ‹∞ ⇔ αα_n+βn ≤ 1, where α>0,α ∈ [0,n), ρ and dμ are the distance function and volume element of H^n respectively., number=1, journal=Journal of Partial Differential Equations, year=2015, month=Mar., pages=39–46