An abnormality diagnosing apparatus for a glow plug 8 provided in an engine 1. The glow plug 8 is energized by power supply from a battery 7 during a glow period from starting of the engine 1 to completion of engine starting. First, on the basis that power output edf from an alternator 12, which is driven to charge the battery 7, is within an appropriate range and that the variation Δedf of the power output edf at the end of the glow period is not more than a reference value a, it is determined if there is a possibility of an abnormality in the glow plug 8. After the determination, the plug 8 is energized temporarily. Then, on the basis that the power output edf is within a modified appropriate range, which has a greater upper limit than the previous appropriate range and that the variation Δedf while the plug 8 is energized is not more than the reference value a, it is determined that the an abnormality actually occurred. Accordingly, failure of determination of the presence of an abnormality due to deterioration of the battery 7 is prevented when an abnormally has actually occurred.