We study the uniqueness of positive solutions of the boundary value problem u ″ + a ( t ) u ′ + f ( u ) = 0 , t ∈ ( 0 , b ) , B 1 ( u ( 0 ) ) − u ′ ( 0 ) = 0 , B 2 ( u ( b ) ) + u ′ ( b ) = 0 , where 0 < b < ∞ , B 1 and B 2 ∈ C 1 ( ℝ ) , a ∈ C [ 0 , ∞ ) with a ≤ 0 on [ 0 , ∞ ) and f ∈ C [ 0 , ∞ ) ∩ C 1 ( 0 , ∞ ) satisfy suitable conditions. The proof of our main result is based upon the shooting method and the Sturm comparison theorem.