Given a directed bipartite graph $$G=(V,E)$$ G = ( V , E ) with a node set $$V=\{s\} \cup V_1 \cup V_2 \cup \{t\}$$ V = { s } ∪ V 1 ∪ V 2 ∪ { t } , and an arc set $$E=E_1\cup E_2\cup E_3$$ E = E 1 ∪ E 2 ∪ E 3 , where $$E_1=\{s\} \times V_1$$ E 1 = { s } × V 1 , $$E_2= V_1 \times V_2$$ E 2 = V 1 × V 2 , and $$E_3=V_2 \times \{t\}$$ E 3 = V 2 × { t } . Chen (1995) presented an $$O(|V| |E| \log (\frac{|V|^2}{|E|}))$$ O ( | V | | E | log ( | V | 2 | E | ) ) time algorithm to solve the parametric bipartite maximum flow problem. In this paper, we assume all arcs in $$E_2$$ E 2 have infinite capacity [such a graph is called closure graph Hochbaum (1998)], and present a new approach to solve the problem, which runs in $$O(|V_1| |E| \log (\frac{|V_1|^2}{|E|}+2))$$ O ( | V 1 | | E | log ( | V 1 | 2 | E | + 2 ) ) time using Gallo et al’s parametric maximum flow algorithm, see Gallo et al. (1989). In unbalanced bipartite graphs, we have $$|V_1| << |V_2|$$ | V 1 | < < | V 2 | , so, our algorithm improves Chens’s algorithm in unbalanced and closure bipartite graphs.