Two-dimensional layered materials are gaining much attention in the field of wastewater purification. Herein, we report the synthesis and characterization of an anion selective copper-aluminum-layered double hydroxide/single-walled carbon nanotubes (CuAl-LDH/SWCNTs) composite for the scavenging of organic dye indigo carmine (IC) from aqueous solution. A facile urea hydrolysis method was used for the controlled growth of the metal hydroxides over the SWCNTs. Structural characterization of the prepared materials was investigated using X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), and X-ray diffraction (XRD) techniques. The obtained results revealed that the CuAl-LDH/SWCNTs composite has a higher potential for the removal of IC in comparison to CuAl-LDH and SWCNTs. The enhanced adsorption capacity of the composite revealed that deposition of CuAl-LDH over SWCNTs increases the active adsorption sites and promotes the interactions between the composite and IC dye anion exchange, electrostatic, π-π, hydrogen bonding Moreover, adsorption kinetics, isotherms, and thermodynamic studies have been also proposed to illustrate the mechanism of the IC adsorption onto the CuAl-LDH/SWCNTs composite. Thermodynamic parameters showed that the adsorption of IC dye onto the CuAl-LDH/SWCNTs composite was exothermic and spontaneous in nature. Intra-particle diffusion was determined to be the rate-limiting step and adsorption of IC followed the Langmuir isotherm model with the maximum monolayer adsorption capacity 294.117 mg g at 20 °C. The results suggest that the CuAl-LDH/SWCNTs composite is a potential material for IC adsorption in aqueous solution.