Reactivity controlled compression ignition (RCCI) combustion employs two fuels with a large difference in auto-ignition properties that are injected at different times to generate a spatial gradient of fuel-air mixtures and reactivity. Researchers have shown that RCCI offers improved fuel efficiency and lower NOx and Soot exhaust emissions when compared to conventional diesel diffusion combustion. The majority of previous research work has been focused on premixed gasoline or ethanol for the low reactivity fuel and diesel for the high reactivity fuel. The increased availability of natural gas (NG) in the US has renewed interest in the application of compressed natural gas (CNG) to heavy-duty (HD) diesel engines in order to realize fuel cost savings and reduce pollutant emissions, while increasing fuel economy. Thus, RCCI using CNG and diesel fuel warrants consideration. A computational study was performed on a 15L HD diesel engine to examine trade-offs of pollutant emissions, fuel consumption, peak cylinder pressure and maximum cylinder pressure rise rate. The results from the model indicated that an RCCI combustion strategy had the potential of 17.5% NOx reduction, 78% soot reduction and a 24% decrease in fuel consumption when compared to a conventional diesel combustion strategy using the same air-fuel ratio (AFR) and exhaust gas recirculation (EGR) rate, at the rated power operating condition. This was attained while meeting peak cylinder pressure and maximum cylinder pressure rise rate constraints.