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We study the uniqueness of positive solutions of the boundary value problem u″+a(t)u′+f(u)=0, t∈(0,b), B1(u(0))−u′(0)=0, B2(u(b))+u′(b)=0, where 0<b<∞, B1 and B2∈C1(â„Â), a∈C[0,∞) with a≤0 on [0,∞) and f∈C[0,∞)∩C1(0,∞) satisfy suitable conditions. The proof of our main result is based upon the shooting method and the Sturm comparison theorem.