  In this paper, we first present the complete list of the singularity types of
the Picard number one Gorenstein log del Pezzo surface and the number of the
isomorphism classes with the given singularity type. Then we give out a method
to find out all singularity types of Gorenstein log del Pezzo surface. As an
application, we present the complete list of the Dynkin type of the Picard
number two Gorenstein log del Pezzo surfaces. Finally we present the complete
list of the singularity type of the relatively minimal Gorenstein log del Pezzo
surface and the number of the isomorphism classes with the given singularity
type.
