An object of the present invention is to determine individually and accurately an ignitability index value and an evaporativity index value of a fuel.A fuel injection valve (12) for which a fuel injection direction is set such that fuel is directed toward a cylinder wall surface (54) is included. An air-fuel ratio (a first air-fuel ratio) of an exhaust gas and a crank angular velocity (a first crank angular velocity) during combustion associated with fuel injection at a first after injection timing T1 are acquired. An air-fuel ratio (a second air-fuel ratio) of the exhaust gas and a crank angular velocity (a second crank angular velocity) during combustion associated with fuel injection at a second after injection timing T2 that is retarded from the first after injection timing T1 are acquired. A cetane number and a distillation property are determined based on Δ A/F that is an amount of change between the first air-fuel ratio and the second air-fuel ratio, Δ crank angular velocity that is an amount of change between the first crank angular velocity and the second crank angular velocity, and predetermined determination basic information.