Let T be a triangular ring. We say that a family of maps δ ={δn, δn : T → T , n ∈ N} is a Jordan higher derivable map (without assumption of additivity or continuity) if δn(AB + BA) = Pi+j=n[δi(A)δj (B) +δj (B)δi(A)] for all A, B ∈ T . In this paper, we show that every Jordan higher derivable map on a triangular ring is a higher derivation. As its application, we get that every Jordan higher derivable map on an irreducible CDCSL algebra or a nest algebra is a higher derivation, and new characterizations of higher derivations on these algebras are obtained.