To survey the anaerobic co-digestion (AcoD) of oil refinery wastewater (ORWW) with sugarcane bagasse (SCB), six different AcoD compositions were evaluated. Results including cumulative biogas production (BGP), bio-methane contents (BMP), and soluble chemical oxygen demand (CODs) removal rate were experimentally obtained. The negligible BGP by ORWW mono-digestion revealed that it could not support any microbial activity. However, increasing the SCB ratio in the AcoD compositions led to increased BGP and BMP contents. By considering the statistical test (LSD0.05) results for the kinetic parameters, the 1:4 ratio treatment was the most favorable AcoD composition. Moreover, the CODs removal rate from 22.34 ± 1.63% for the SCB mono-digestion was improved to 49.67 ± 0.38% for the 2:3 AcoD composition and BMP content from 54.12 ± 0.45% for the SCB mono-digestion was enhanced to 62.69 ± 1.22% for the 1:4 AcoD composition with 20% lower SCB usage. The results computed by applying three mathematical models determined that the modified Gompertz model provided the best fit. Also, implementing artificial neural network algorithms to model the BGP data revealed that the Back Propagation algorithm was the best suited for the experimental BGP data, with 0.6444 and 0.9658 for MSE and R2, respectively.