A fundamental understanding of the relationship between chemical composition and combustion quality may provide an improved means of assessing fuel combustion characteristics. As such, a fuel parameter based on the average molecular structure of multi-component fuels, including petroleum-derived fuels and alternative fuels such as bio-fuel, is applied to predict both ignition and anti-knock quality. This parameter is derived from proton nuclear magnetic resonance (1H-NMR) analysis indicating hydrogen type distribution of fuel molecules. The predicted cetane number (PCN) calculated by the equation developed with 1H-NMR in this study shows a good correlation to the cetane number for a wide range of fuels. The appropriateness of the prediction model was confirmed with the following considerations. 1) A fundamental consideration on the effects of hydrocarbon types on cetane numbers. 2) The application of the model to other fuels, excluding those used in the development of the model. 3) The blending of cetane number behavior for typical diesel fuel components. The prediction models for both research octane number (RON) and motor octane number (MON) are also developed with 1H-NMR analysis and average molecular weight. Although the models give a good correlation, there seems to be room for improvement. Both of PCN and CN are highly correlated to the ignition delay measured with DI diesel engines operated under premixed charge compression ignition (PCI) conditions. The PCN can be applied to the ignition delay obtained by PCI operation. This study suggests that both the ignition and anti-knock qualities are highly controlled by the average molecular structure and molecular weight of fuels, regardless of fuel source and composition.