We are concerned with the higher-order nonlinear three-point boundary value problems: x ( n ) = f ( t , x , x ′ , … , x ( n − 1 ) ) , n ≥ 3 , with the three point boundary conditions g ( x ( a ) , x ′ ( a ) , … , x ( n − 1 ) ( a ) ) = 0 ; x ( i ) ( b ) = μ i , i = 0 , 1 , … , n − 3 ; h ( x ( c ) , x ′ ( c ) , … , x ( n − 1 ) ( c ) ) = 0 , where a < b < c , f : [ a , c ] × ℝ n → ℝ = ( − ∞ , + ∞ ) is continuous, g , h : ℝ n → ℝ are continuous, and μ i ∈ ℝ , i = 0 , 1 , … , n − 3 are arbitrary given constants. The existence and uniqueness results are obtained by using the method of upper and lower solutions together with Leray-Schauder degree theory. We give two examples to demonstrate our result.