We have measured the field-driven velocity of chiral Néel domain walls (DWs) stabilized by the Dzyaloshinskii–Moriya interaction (DMI) in a Pt/Co/Ta/Pt film with perpendicular magnetic anisotropy. A simple model based on the universal creep theory allows us to describe the anisotropic propagation of a DW along the contour of a bubble domain, driven by an out-of-plane field in the presence of a static in-plane field. This model is used to obtain the DMI constant from the measurement of the DW propagation with only one value of the in-plane field, simplifying the existing method relying on several measurements. The DMI constant extracted from the model is in good agreement with independent measurements.