A combustion timing prediction method for a compression self-ignition internal combustion engine that causes a hydrocarbon fuel in a combustion chamber to perform compression self-ignition, with which a combustion timing of the hydrocarbon fuel used in the compression self-ignition internal combustion engine is predicted, comprising the steps of: specifying a proportion of each of four types of hydrocarbon components consisting of paraffin hydrocarbon, aromatic hydrocarbon, olefin hydrocarbon, and naphthene hydrocarbon contained in the hydrocarbon fuel; calculating, on the basis of a motor octane number (MON i) of each of the hydrocarbon components and a compression top dead center temperature (T TDC) in the combustion chamber of the internal combustion engine, a value of a first function (F1 i) serving as a function of the motor octane number (MON i) and the compression top dead center temperature (T TDC) for each of the hydrocarbon components; determining a coefficient (C i) indicating a reaction acceleration effect or a reaction suppression effect of the respective hydrocarbon component relative to a reaction of the paraffin hydrocarbon, whereby the values of the coefficient (C i) vary in accordance with the intake air temperature, and calculating, on the basis of the first function (F1 i), the proportion and the coefficient (C i) relating to each of the hydrocarbon components, a value of a second function (F2 i), which is a function that increases in value in response to an increase of the value of any one of the first function (F1 i), the proportion and the coefficient (C i), for each of the hydrocarbon components; integrating the values of the second function (F2 i) relating to the respective hydrocarbon components; and predicting, on the basis of the integrated value of the values of the second function (F2 i), the combustion timing of the hydrocarbon fuel in the internal combustion engine to be later as the integrated value increases. specifying a proportion of each of four types of hydrocarbon components consisting of paraffin hydrocarbon, aromatic hydrocarbon, olefin hydrocarbon, and naphthene hydrocarbon contained in the hydrocarbon fuel; calculating, on the basis of a motor octane number (MON i) of each of the hydrocarbon components and a compression top dead center temperature (T TDC) in the combustion chamber of the internal combustion engine, a value of a first function (F1 i) serving as a function of the motor octane number (MON i) and the compression top dead center temperature (T TDC) for each of the hydrocarbon components; determining a coefficient (C i) indicating a reaction acceleration effect or a reaction suppression effect of the respective hydrocarbon component relative to a reaction of the paraffin hydrocarbon, whereby the values of the coefficient (C i) vary in accordance with the intake air temperature, and calculating, on the basis of the first function (F1 i), the proportion and the coefficient (C i) relating to each of the hydrocarbon components, a value of a second function (F2 i), which is a function that increases in value in response to an increase of the value of any one of the first function (F1 i), the proportion and the coefficient (C i), for each of the hydrocarbon components; integrating the values of the second function (F2 i) relating to the respective hydrocarbon components; and predicting, on the basis of the integrated value of the values of the second function (F2 i), the combustion timing of the hydrocarbon fuel in the internal combustion engine to be later as the integrated value increases.