In this paper, the influence of hydrogen addition or substitution on Conventional Diesel Combustion (CDC) and Reactivity Controlled Compression Ignition (RCCI) combustion at 1208 and 1300 rpm on medium load, without exhaust gas recirculation (EGR) in Caterpillar 3401 heavy-duty diesel engine is numerically investigated. Different parameters of the ringing intensity, heat efficiency, heat release, cylinder pressure variations, CO, soot, UHC, NOx, and CO2 emissions are studied and compared with and without hydrogen combustion. It results that in CDC at 1208 rpm, if hydrogen is substituted to 40.2% of diesel input energy, the emission of CO, soot, UHC, NOx and CO2 greenhouse will decrease to 98%, 27%, 99%, 13% and 38%, respectively; however, indicated work suffers 1% reduction. On the other hand, in all states of hydrogen addition in CDC at 1208 rpm, all pollutant emissions increase, but, this addition leads to increasing of output work. In the best case when hydrogen is added to diesel by 55% of input energy, work increases by 43%; however, when hydrogen is added over than 55% of input energy, knocking will happen. In RCCI combustion, when hydrogen is added or substituted, instead of methane and diesel respectively, methane combustion will improve and emissions except NOx, will reduce. Hydrogen addition in RCCI combustion at 1300 rpm causes the increment of chamber reactivity, which leading to advance the ignition and hasten the rate of temperature and pressure rise in the chamber. The important result is that the hydrogen substitution more than 11% of input energy for methane, and hydrogen addition more than 60% of input energy for diesel cause knocking phenomenon in RCCI engine. In the final, to make a comprehensive comparison the performance and pollutions of gasoline-diesel, methane-diesel, methane-diesel-hydrogen and diesel-hydrogen combustions in this engine are compared among several studies.