Using the theory of coincidence degree, we establish existence results of positive solutions for higher-order multi-point boundary value problems at resonance for ordinary differential equation u ( n ) ( t ) = f ( t , u ( t ) , u ′ ( t ) , … , u ( n − 1 ) ( t ) ) + e ( t ) ,       t ∈ ( 0 , 1 ) , with one of the following boundary conditions: u ( i ) ( 0 ) = 0 , i = 1 , 2 , … , n − 2 , u ( n − 1 ) ( 0 ) = u ( n − 1 ) ( ξ ) , u ( n − 2 ) ( 1 ) = ∑ j = 1 m − 2 β j u ( n − 2 ) ( η j ) , and u ( i ) ( 0 ) = 0 , i = 1 , 2 , … , n − 1 , u ( n − 2 ) ( 1 ) = ∑ j = 1 m − 2 β j u ( n − 2 ) ( η j ) , where f : [ 0 , 1 ] × ℝ n → ℝ = ( − ∞ , + ∞ ) is a continuous function, e ( t ) ∈ L 1 [ 0 , 1 ] β j ∈ ℝ   ( 1 ≤ j ≤ m − 2 ,   m ≥ 4 ) , 0 < η 1 < η 2 < ⋯ < η m − 2 < 1 , 0 < ξ < 1 , all the β − j − s have not the same sign. We also give some examples to demonstrate our results.