By using the fixed-point index theorem, we consider the existence of positive solutions for the following nonlinear higher-order four-point singular boundary value problem on time scales u Δ n ( t ) + g ( t ) f ( u ( t ) , u Δ ( t ) , … , u Δ n − 2 ( t ) ) = 0 , 0 < t < T ; u Δ i ( 0 ) = 0 , 0 ≤ i ≤ n − 3 ; α u Δ n − 2 ( 0 ) − β u Δ n − 1 ( ξ ) = 0 , n ≥ 3 ; γ u Δ n − 2 ( T ) + δ u Δ n − 1 ( η ) = 0 , n ≥ 3 , where α > 0 , β ≥ 0 , γ > 0 , δ ≥ 0 , ξ , η ∈ ( 0 , T ) , ξ < η , and g : ( 0 , T ) → [ 0 , + ∞ ) is rd-continuous.