There has been a lot of attention on water pollution by dyes in recent years because of their serious toxicological implications on human health and the environment. Therefore, the current study presented a novel polyethylene glycol-functionalized graphene oxide/chitosan composite (PEG-GO/CS) to remove dyes from aqueous solutions. Several characterization techniques, such as SEM, TEM, FTIR, TGA/DTG, XRD, and XPS, were employed to correlate the structure–property relationship between the adsorption performance and PEG-GO/CS composites. Taguchi’s (L25) approach was used to optimize the batch adsorption process variables [pH, contact time, adsorbent dose, and initial concentration of methyl orange (MO)] for maximal adsorption capacity. pH = 2, contact time = 90 min, adsorbent dose = 10 mg/10 mL, and MO initial concentration = 200 mg/L were found to be optimal. The material has a maximum adsorption capacity of 271 mg/g for MO at room temperature. With the greatest R2 = 0.8930 values, the Langmuir isotherm model was shown to be the most appropriate. Compared to the pseudo-first-order model (R2 = 0.9685), the pseudo-second-order model (R2 = 0.9707) better fits the kinetic data. Electrostatic interactions were the dominant mechanism underlying MO sorption onto the PEG/GO-CS composite. The as-synthesized composite was reusable for up to three adsorption cycles. Thus, the PEG/GO-CS composite fabricated through a simple procedure may remove MO and other similar organic dyes in real contaminated water.