Let a ∈ C[0, 1], b ∈ C([0, 1], (−∞, 0)). Let φ1(t) be the unique solution of the linear boundary value problem u"(t)+ a(t)u'(t)+b(t)u(t) = 0, t∈(0, 1), u(0) = 0, u(1) =1. We study the existence of positive solutions to the nonlinear boundary-value problem u"(t)+ a(t)u'(t)+b(t)u(t) +h(t)f (u) = 0, t∈ (0, 1), u(0) = 0, αu(η)= u(1), where 0 <η<1and 0<αφ1(η)< 1 are given, h ∈ C([0, 1], [0,∞]) satisfying that there exists x0 ∈ [0, 1] such that h(x0)> 0, and f ∈ C([0,∞], [0,∞]). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.