A dielectric barrier discharge in neon at atmospheric pressure is investigated with electrical measurement and fast photography. It is found that a stable diffuse discharge can be easily generated in a gap with a gap space of 0.5-6 mm and is identified with a glow discharge. The first breakdown voltage of the gap is considerably higher than that of the same gap working in a stable diffuse discharge mode, which indicates that Penning ionization of neon metastables from the previous discharge with inevitable gas impurities plays an important role in the decrease in the breakdown voltage. Discharge patterns are observed in a gap shorter than 1 mm. From the experiments with a wedge-like gap, it is found that the discharge patterns are formed in the area with a higher applied electric field, which suggests that a higher applied electric field may cause a transition from a diffuse glow to discharge patterns.