Amongst many chemical pollutants that cause environmental pollution, the presence of organic dyes in water resources can cause substantial health issues. Thus, owing to their mutagenicity and their adverse effects on human health, environment, and animals, they must be removed from industrial wastewater. In this study, UiO-66 metal–organic framework, as well as composite nanoparticles with carbonaceous materials such as MWCNTs-COOH and graphene oxide (GO) with different molar ratios (2.9 and 5.8 wt.%), were synthesized through solvothermal method since carbonaceous materials are an emerging material that demonstrates improvement in the properties of adsorbents. Then, the synthesized materials were utilized as a solid adsorbent for removing four different dyes including; anionic methyl red (MR), anionic methyl orange (MO), cationic methylene blue (MB), and cationic malachite green (MG) prepared from distilled water. The properties of prepared adsorbents were characterized via X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), field emission scanning electron microscopy (FESEM), Photoluminescence spectroscopy (PL), Brunauer–Emmett–Teller (BET), as well as surface area analyzer and energy dispersive spectroscopy (EDS-MAP). Further, the influences of various factors including initial concentrations of the dyes and adsorption process time on adsorption of dyes were investigated. Adsorption experiments indicated that synthesized adsorbents exhibited the highest adsorption efficiency towards MR and MO dyes. Moreover, the experimental adsorption results revealed that MWCNTs-UiO-66 nanocomposites could adsorb 98% of MR and MO as well as 72% of MB and 46% of MG. Furthermore, the kinetic and stability of the materials over time were investigated. To reach a clear picture, adsorption experiments demonstrated that the amount of dye uptake on adsorbents was enhanced by increasing the contact time as well as uptake of materials with time were stable for both cationic and anionic dyes. The MR, MO, and MB adsorption isotherms were fitted with the Langmuir and Freundlich models. The Langmuir showed the highest agreement in these dyes and MWCNTs-UiO-66 (2.9 and 5.8 wt.%) exhibited a maximum adsorption capacity of 105.26 mg/g for MR, while the MG isotherm was in line with the Langmuir model.