As a popular low-temperature plasma source, dielectric barrier discharge (DBD) has drawn significant attention due to its extensive application field including surface modification, material synthesis, sterilization, etc. DBD has presented different modes with varying experimental conditions. In order to address the formation mechanism of the different modes, a two-dimensional axis-symmetric fluid model is employed to simulate the characteristics of DBD in atmospheric pressure argon. Results indicate that DBD undergoes a scenario from a discretely-filamentary mode, a diffuse mode, a complementarily-filamentary mode, to a columnar mode with increasing voltage amplitude (V_a) or discharge power (P_dis). Waveforms of applied voltage and discharge current indicate that for every discharge mode, the discharge current waveforms are always symmetrical for positive and negative discharge half-cycles. The discharge current exhibits single-pulse characteristics per half-cycle with low V_a (or P_dis), and turns to double-pulse, triple-pulse, or multi-pulse characteristics per half-cycle with increasing V_a (or P_dis). Spatial-temporal evolutions of electron density and electric field reveal that residual electrons play an important role in the discharge mode. Electric field (E) is mainly composed of its axial component, and its radial component only appears at the edge of the electrode in the diffuse mode. In the complementarily-filamentary mode, the locations of the strong-MDs and those of the weak-MDs alternate in the consecutive half-cycles. The strong-MD channels are stationary at fixed locations in the consecutive half-cycles for the columnar mode. In addition, the diameter of residual electrons in the columnar mode is larger than that in the filamentary mode. Moreover, the generation rate of Ar^* increases, while the energy efficiency of the discharge shrinks with increasing V_a (or P_dis). These results are of great significance for the deep understanding of discharge mode and the improving of DBD performance.