<p>In oil and gas well drilling engineering, a near-borehole acoustic velocity model could be used for quantifying the radial distance of drilling fluid intrude into the formation rocks. Therefore, for the high time cost drilling engineering projects, it is necessary to obtain the near-borehole velocity model as quickly as possible to evaluate the drilling fluid intrusion distance. In this paper, we propose a traveltime tomographic method to quickly build the velocity model around the borehole using the array acoustic logging data. The ray tracing process of the method is based on the finite-difference computational scheme of the fast sweeping method, which is much more efficient compared with the conventional two-point ray tracing methods because the proposed method considers contributions of all ray paths corresponding to the same source transducer simultaneously. Furthermore, this paper proposes to widen the ray path by rotating finite-differential directions, so as to enlarge the coverage area of the inversion gradient. The strategy significantly reduces the number of iterations needed for model convergence. Synthetic and field data tests prove that the proposed near-borehole acoustic velocity model inversion method has high computational efficiency, and is applicable for quantifying the radial distance of drilling fluid intrude into the formation rocks in the time-sensitive drilling process.</p>