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In this article, batch adsorption of methyl orange and acid blue-2445 from the binary system onto the anion exchange membrane (BI) was studied at room temperature. The effect of endowment including membrane dosage, contact time, and initial concentration on the percentage removal of dye was investigated. The percentage of dye removal increased with the increase in contact time and reached a maximum after 2 h. The optimum membrane dosage for removal of these anionic dyes was found to be 0.3 g with the rise of temperature from 283–323 K. Experimental results were subjected to non-linear and linear forms of several isotherms such as Freundlich, Langmuir, Temkin, Dubinin–Radushkevich, Harkin’s–Jura, Halsey, Flory–Huggins, Hill, Toth, Sips, and Redlich–Peterson isotherms. The Langmuir adsorption capacity was computed from a linear and non-linear form of isotherms. The thermodynamic parameters indicated that the adsorption of methyl orange and acid blue-2445 is both thermodynamically spontaneous in nature. The positive value of enthalpy changes exhibited endothermic nature for the adsorption of methyl orange and acid blue-2445 on anion exchange membrane BI. These results showed that anion exchange membrane BI could be used for wastewater management. [ABSTRACT FROM AUTHOR]