Transversely isotropic (TI) models have become essential in generating accurate depth images from seismic data. Here, we develop image-domain tomography (IDT) for building acoustic VTI (TI with a vertical symmetry axis) models from P-wave reflection data. Based on a separable dispersion relation, the modeling operator extrapolates only P-wavefields without the shear-wave artifacts. The inversion algorithm includes least-squares reverse-time migration (LSRTM), which improves the quality of the extended images and accuracy of parameter estimation. Whereas the zero-dip NMO velocity (V) and anellipticity parameter η are updated by focusing energy in space-lag LSRTM gathers, the Thomsen parameter δ is constrained by image-guided interpolation between two or more boreholes. We also apply image-guided smoothing to the IDT gradients of V and η to steer the inversion towards geologically plausible models. To mitigate the trade-off between V and η, we adopt a multistage approach that gradually relaxes the constraints on the spatial η-variation. The robustness of the algorithm is demonstrated on the elastic VTI Marmousi-II model. We also present preliminary inversion results for a line from a 3D data set acquired in the Gulf of Mexico.