The pinning and depinning of antiferromagnetic (AFM) domain wall is certainly the core issue of AFM spintronics. In this work, we study theoretically the Neel-type domain wall pinning and depinning at a notch in an antiferromagnetic (AFM) nano-ribbon. The depinning field depending on the notch dimension and intrinsic physical parameters are deduced and also numerically calculated. Contrary to conventional conception, it is revealed that the depinning field is remarkably dependent of the damping constant and the time-dependent oscillation of the domain wall position in the weakly damping regime benefits to the wall depinning, resulting in a gradual increase of the depinning field up to a saturation value with increasing damping constant. A one-dimensional model accounting of the internal dynamics of domain wall is used to explain perfectly the simulated results. It is demonstrated that the depinning mechanism of an AFM domain wall differs from ferromagnetic domain wall by exhibiting a depinning speed typically three orders of magnitude faster than the latter, suggesting the ultrafast dynamics of an AFM system.