  The Manin-Peyre conjecture is established for a split singular quintic del
Pezzo surface with singularity type $\mathbf{A}_2$ and two split singular
quartic del Pezzo surfaces with singularity types $\mathbf{A}_3+\mathbf{A}_1$
and $\mathbf{A}_4$ respectively. We use a unified and different slightly method
from the previous and improve their error terms. Our method is general and can
handle most of singular del Pezzo surfaces of degree $d\geq 3$.
