  We classify del Pezzo non-commutative surfaces that are finite over their
centres and have no worse than canonical singularities. Using the minimal model
program, we introduce the minimal model of such surfaces. We first classify the
minimal models and then give the classification of these surfaces in general.
This presents a complementary result and method to the classification of del
Pezzo orders over projective surfaces given by Chan and Kulkarni in 2003
