This apparatus detects, during a detection period from an intermediate timing (a time point t11) between respective compression top dead center timings of two of the cylinders that are successive to each other in ignition sequence to a timing (a time point t12) immediately before the start of fuel injection into that one of those cylinders which is later in ignition sequence, a fuel pressure by a pressure detection sensor that is provided in a manner corresponding to the cylinder that is later in ignition sequence, and determines, on the basis of a speed of decrease in the detected fuel pressure PQ, whether or not there has occurred an abnormality of fuel leakage.