This paper is focused on the utilization of hybrid catalysts obtained from layered double hydroxides containing molybdate as the compensation anion (Mo-LDH) and graphene oxide (GO) in advanced oxidation using environmentally friendly H2O2 as the oxidation agent for the removal of indigo carmine dye (IC) from wastewaters at 25 °C using 1 wt.% catalyst in the reaction mixture. Five samples of Mo-LDH-GO composites containing 5, 10, 15, 20, and 25 wt% GO labeled as HTMo-xGO (where HT is the abbreviation used for Mg/Al in the brucite type layer of the LDH and x stands for the concentration of GO) have been synthesized by coprecipitation at pH 10 and characterized by XRD, SEM, Raman, and ATR-FTIR spectroscopy, determination of the acid and base sites, and textural analysis by nitrogen adsorption/desorption. The XRD analysis confirmed the layered structure of the HTMo-xGO composites and GO incorporation in all samples has been proved by Raman spectroscopy. The most efficient catalyst was found to be the catalyst that contained 20%wt. GO, which allowed the removal of IC to reach 96.6%. The results of the catalytic tests indicated a strong correlation between catalytic activity and textural properties as well as the basicity of the catalysts.