In a dual-fuel internal combustion engine which can selectively use gaseous fuel such as CNG or liquid fuel such as gasoline, a pair of intake passages are independently connected to a combustion chamber of the engine, and a gaseous fuel supply device and a liquid fuel supply device are provided in the corresponding intake passages so that the liquid and gaseous fuels may not mix with each other when the fuel for the engine is switched over one from the other as they are introduced into the combustion chamber through different intake passages. Further, by switching the operating mode of the intake valve when changing the fuel, the configuration of the intake passage can be optimized for each fuel, and the timing and the lift of the intake valves may also be optimized for each fuel without complicating the control structure of the overall system. The present invention can improve the torque output and the emission property of the dual-fuel engine.