We are concerned with the nonlinear fourth-order three-point boundary value problem u ( 4 ) ( t ) = a ( t ) f ( u ( t ) ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = 0 , α u ″ ( η ) − β u ‴ ( η ) = 0 , γ u ″ ( 1 ) + δ u ‴ ( 1 ) = 0 . By using Krasnoselskii's fixed point theorem in a cone, we get some existence results of positive solutions.