In this study, the effect of adding hydrogen to natural gas and EGR ratio was conducted on a diesel engine to investigate the engine performance and exhaust gases by AVL Fire multi-domain simulation software. For this investigation, a mixture of hydrogen fuel and natural gas replaced diesel fuel. The percentage of hydrogen in blend fuel changed from 0% to 40%. The compression ratio converted from 17:1 to 15:1. The EGR ratios were in three steps of 5%, 10%, and 15%, with different engine speeds from 1000 to 1800 RPM. The Gaussian process regression (GPR) was developed to model engine performance and exhaust emissions. The optimal values of EGR and the percentage of hydrogen in the blend of HCNG were extracted using a multi-objective genetic algorithm (MOGA). The results showed that by increasing EGR, thermal efficiency, the engine power, and specific fuel consumption decreased due to prolongation of combustion length while cumulative heat release increased but, its effect on cylinder pressure is insignificant. Adding hydrogen to natural gas increased the combustion temperature and, consequently NOx. While the amount of CO and HC decreased. The results of GPR and MOGA illustrated that at different engine speeds, the optimum values of EGR and HCNG were 6.35% and 31%, respectively.