A new surface dielectric barrier discharge source containing a matrix of holes in the dielectric slice is put forward in this paper, for which the plasma characteristics and the delivery of reactive species to the downstream sample are studied for three experimental conditions, i.e., EC1 with a helium gas flow of 1 SLM through the holes, EC2 with an artificial air flow of 1 SLM, and EC3 without any gas flow. All the other conditions are kept the same. For the same discharge power of 2 W, it is found that the surface plasma in EC1 is comparatively more homogeneous, the discharge voltage is lower by ~12%, and the densities of reactive species are much higher, since the emission spectral lines of N2(C), N2+(B), He(3s3S), and O(3p5P) are stronger by at least sixfold. A petri dish of deionized water is put 5-mm downstream the surface discharge, in which the concentrations of nitrite, nitrate, H2O2, and NO are measured after the plasma treatment of 3 min. Compared with EC1, EC2, and EC3, it is found that the gas flow can increase the concentration of H2O2 by ~1.4-fold, but when helium is participated, a further increase of sixfold is achieved. Similarly, further increase is also found for the other three reactive species, which may be ascribed to the higher densities of gaseous reactive oxygen and nitrogen species in the helium-participated plasma and their larger diffusion coefficients in helium compared with that in air.