Acoustic logging is an effective solution to obtain the radial formation velocity profile near a borehole, and it is critical for borehole stability evaluation and production performance monitoring. Herein, the responses of monopole acoustic logging while drilling (LWD) in a fluid-filled borehole surrounded by homogeneous and heterogeneous formations are numerically simulated using the finite difference algorithm in a cylindrical coordinate system. A stepwise inversion method is proposed to determine radial formation velocity distributions near the borehole based on the acoustic LWD data as follows. The heterogeneous formation around the borehole is approximated as multi-layered media with different elastic parameters, and then the slowness time correlation (STC) algorithm is applied to determine the compressional (P) and shear (S) wave velocities corresponding to different offsets. Finally, the thickness of each layer is determined according to the ray theory. Influences of measurement environment parameters, such as the central frequency of the source, thickness of the formation variation zone and elastic parameter changes of the formation variation zone, on the inversion results are evaluated to confirm the applicability of the proposed stepwise inversion method. The numerical simulation results demonstrate that refracted P-, refracted S- and Stoneley waves exhibit specific responses to the heterogeneity of the near-borehole formation, whereas collar waves are minimally influenced by the formation properties. The formation velocities do not change with the offset in the homogeneous formation models, although stepped changes are observed in the heterogeneous formation models. Short-offset waveforms are affected by the properties of the formation close to the borehole wall, whereas long-offset waveforms are primarily affected by the properties of the original formation. Relationships between the formation velocities and the offset can be converted into the radial formation velocity distributions by calculating the arrival times of waves propagating along different ray paths. Under common survey conditions, the inversion result of each model is similar to its real velocity distribution, which confirms the effectiveness of the proposed stepwise inversion method. This study thus provides a theoretical basis for developing 3D acoustic LWD tools.