Summary: The delta shock wave for a simplified chromatography system is obtained in the Riemann solution when \(- 1 < v_- < 0 < v_+\). In fact, the result in this paper is the reasonable generalization of the result in [\textit{M. Sun}, Q. Appl. Math. 69, No. 3, 425--443 (2011; Zbl 1237.35114)] with \(v_- = 0 < v_+\) which is exactly the critical situation for \(- 1 < v_- < 0 < v_+\). The self-similar viscosity vanishing approach is also used to check the delta shock wave solution.