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By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: −u′′(t)=λ[f(t,u(t))−q(t)], 0<t<1, αu(0)−βu′(0)=∫01u(s)dξ(s), γu(1)+δu′(1)=∫01u(s)dη(s), where λ>0 is a parameter; f:(0,1)×(0,∞)→[0,∞) is continuous; f(t,x) may be singular at t=0, t=1, and x=0, and the perturbed term q:(0,1)→[0,+∞) is Lebesgue integrable and may have finitely many singularities in (0,1), which implies that the nonlinear term may change sign.