The zinc sulfide/copper oxide–carbon nanotube nanocomposite (ZnS/CuO-CNT) was fabricated by using an in-situ hydrothermal synthesis method and was used for simultaneous ultrasound-assisted adsorptive removal of a binary mixture of ponceau 4R (P4R) and tartrazine (TA) acid food dyes from contaminated water. The as-synthesized ZnS/CuO-CNT was described by FESEM, XRD, FTIR, BET, and zeta potential analysis. The results included nested network morphology, high purity with the crystalline structure, oxygen-containing functional groups, mesoporous/micropores texture with cumulate interspace, specific surface area of 106.54 m2 g-1, and zero-point charge (pHzpc) of 5.3. In adsorption experiments, the simultaneous effect of main independent variables, including solution pH, adsorbent dosage, concentration of each dye, temperature, and sonication time on the removal efficiency of dyes was studied systematically using the central composite design (CCD) method based on response surface methodology (RSM). Also, the second-order multivariate equation was presented to determine the relationship between the removal efficiencies of P4R and AT dyes and six independent effective variables. The high correlation coefficient (R2 ≥ 0.99), significant p-value (P < 0.0001), and non-significant lack-of-fit (P > 0.05) showed the high accuracy, and validity of the proposed model to predict the removal efficiency of P4R and TA acid food dyes. The experimental removal efficiency for P4R and TA dyes was found to be 98.45 ± 2.54, and 99.21 ± 2.23, respectively. Also, the Langmuir maximum adsorption capacity for P4R and TA dyes was determined to be 190.1 mg g-1 and 183.5 mg g-1, respectively. Finally, the adsorbent's reusability was tested for six periods and could be reused repeatedly without significant reduction in adsorption performance.