In this paper, a fixed point theorem in a cone and some inequalities of the associated Green’s function are applied to obtain the existence of positive solutions of second-order three-point boundary value problem with dependence on the first-order derivative \t\t\tx″(t)+f(t,x(t),x′(t))=0,0<t<1,x(0)=0,x(1)=μx(η),\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned}& x''(t) + f\\bigl(t, x(t), x'(t)\\bigr) =0, \\quad 0< t< 1, \\\\& x(0) =0, \\qquad x(1) =\\mu x(\\eta ), \\end{aligned}$$ \\end{document} where f: [0, 1] times [0, infty ) times R rightarrow [0, infty ) is a continuous function, mu >0, eta in (0, 1), mu eta <1. The interesting point is that the nonlinear term is dependent on the convection term.