Biodiesel offers several advantages over conventional diesel, including a higher cetane number and inherent oxygen content, while natural gas, due to its abundance and lower emissions, serves as a promising alternative fuel for dual-fuel engines. This numerical study investigates a dual-fuel engine powered by biodiesel and natural gas, with hydrogen and oxygen enrichment levels ranging from 3% to 12% and 3%-30%, respectively using Converge software. The results demonstrate that the addition of 12% hydrogen (share energy) leads a significant reduction in unburned hydrocarbon emissions by 40%, and lowers carbon monoxide levels. Also, the burning interval decreases from 15.2 to 9.4 CA with the increase of hydrogen. Furthermore, hydrogen enrichment of 12% increases thermal efficiency from 47.3% to 47.9%. Moreover, increasing oxygen concentration from 3% to 30% leads to a 75% reduction in unburned hydrocarbons and a 60% decrease in soot formation. The ignition delay is also shortened from 10.5 degrees CA to 9.3 degrees CA. Moreover, the indicated mean effective pressure exhibited a modest improvement of 1.1%.