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The ejecta velocity is a very important parameter in studying the structure and properties of Type Ia supernovae (SNe Ia). It is also a candidate key parameter in improving the utility of SNe Ia for cosmological distance determinations. Here we study the velocity distribution of a sample of 311 SNe Ia from the kaepora database. The velocities are derived from the Si II $λ$6355 absorption line in optical spectra measured at (or extrapolated to) the time of peak brightness. We statistically show that the observed velocity has a bimodal Gaussian distribution consisting of two groups of SNe Ia: Group I with a lower but narrower scatter ($μ_1 = 11000 \text{km s}^{-1}$, $σ_1 = 700 \text{km s}^{-1}$), and Group II with a higher but broader scatter ($μ_2 = 12300 \text{km s}^{-1}$, $σ_2 = 1800 \text{km s}^{-1}$). The population ratio of Group I to Group II is 201:110 (65%:35%). There is substantial degeneracy between the two groups, but for SNe Ia with velocity $v > 12000 \text{km s}^{-1}$, the distribution is dominated by Group II. The true origin of the two components is unknown, though there could be that naturally there exist two intrinsic velocity distributions as observed. However, we try to use asymmetric geometric models through statistical simulations to reproduce the observed distribution assuming all SNe Ia share the same intrinsic distribution. In the two cases we consider, 35\% of SNe Ia are considered to be asymmetric in Case 1, and all SNe Ia are asymmetric in Case 2. Simulations for both cases can reproduce the observed velocity distribution but require a significantly large portion ($>35\%$) of SNe Ia to be asymmetric. In addition, the Case 1 result is consistent with recent polarization observations that SNe Ia with higher Si II $λ$6355 velocity tend to be more polarized.