Multi-pulse atmospheric-pressure glow discharges between two slightly unparallel electrodes were carried out in helium. The mode of discharge was investigated using an intensified charge-coupled device camera. The discharge current through gas gap and surface charge on the solid dielectric barrier were calculated. Based on analysis of surface charge on the solid barrier, space charges in gas gap, applied voltage across electrodes and field strength in gas gap, the formation mechanism of multi-pulse discharge was discussed. The discharge evolution pictures show that discharge is generated at the narrower side. At the other side, discharge is also generated at the first current peak. Physical process of the first pulse of atmospheric-pressure glow discharge in helium starts from a Townsend discharge leading to a glow discharge, and that of each subsequent current pulse is a glow discharge. Between two consecutive current pulses, a faint glow discharge is maintained in the gas gap. Theoretical analysis shows that multi-pulse discharge is a result of co-evolution of both surface charge as well as space charge and applied voltage, and the Townsend discharge does not appear during current pulse sequence of the same half cycle, except for discharge inception.