Full waveform inversion (FWI) in transversely isotropic media with a vertical symmetry axis (VTI) provides an opportunity to better match the data at the near and far offsets. However, multiparameter FWI, in general, suffers from serious cycle-skipping and trade-off problems. Reflection waveform inversion (RWI) can help us recover a background model by projecting the residuals of reflections along the reflection wavepath. Thus, we extend RWI to acoustic VTI media utilizing the proper parameterization for reduced parameter tradeoff. From a radiation patterns analysis, an acoustic VTI medium is better described by a combination of the normal-moveout velocity v n and the anisotropic parameters η and δ for RWI applications. We design a three-stage inversion strategy to construct the optimal VTI model. In the first stage, we only invert for the background v n by matching the simulated reflections from the perturbations of v n and δ with the observed reflections. In the second stage, the background v n and η are optimized simultaneously and the far-offset reflections mainly contribute to their updates. We perform Born modelling to compute the reflections for the two stages of RWI. In the third stage, we perform FWI for the acoustic VTI medium to delineate the high-wavenumber structures. For this stage, the VTI medium is described by a combination of the horizontal velocity v h , η and ε instead of v n , η and δ. The acoustic VTI FWI utilizes the diving waves to improve the background, as well as utilizes the reflections for high-resolution information. Finally, we test our inversion algorithm on the modified VTI Sigsbee 2A model (a salt free part) and a 2D line from a 3D Ocean Bottom Cable dataset. The results demonstrate that the proposed VTI RWI approach can recover the background model for acoustic VTI media starting from an isotropic model. This background VTI model can mitigate the cycle skipping of FWI and help the inversion recover higher-resolution structures.