By using the Krein-Rutman theorem and Dancer global bifurcation theory, the author studies the global structure of positive solutions for nonlinear third-order three-point boundary value problem { u‴(t)+rf(t,u(t))=0, t∈ (0,1), u(0)=αu′(0), u(1)=βu(η), u′(1)=0, where r>0 is a parameter, 0<η<1,α,β>0,and the nonlinear term f∈C([0,1]×[0,∞),[0,∞)) satisfies asymptotic linear growth condition at 0 and ∞.