In this paper, we consider singularly perturbed boundary-value problems for second-order ordinary differential equations with discontinuous source term arising in the chemical reactor theory. A parameter-uniform error bound for the solution is established using the streamline-diffusion finite-element method on piecewise uniform meshes. We prove that the method is almost second-order convergence for solution and first-order convergence for its derivative in the maximum norm, independently of the perturbation parameter. Numerical results are provided to substantiate the theoretical results.