A localizing gradient damage model with micro inertia effect is proposed for the dynamic fracture of quasi-brittle materials. The objective is to achieve mesh independent solutions, and to avoid spurious effects associated with the conventional nonlocal enhancement. The proposed localizing gradient damage model closely resembles the conventional gradient enhancement, albeit with an interaction domain that decreases with damage, complemented by a micro inertia effect. The tensile loading of a Polymethyl Methacrylate plate is considered. It is shown that the proposed model effectively captures the experimentally observed transition of crack profiles as the loading rate increases, i.e. from a straight crack propagation, to sub-branching, and finally to macro branching. Numerical results in terms of crack patterns, crack velocities, and fracture energies are in good agreement with the experimental data.