Seismic inversion is an important method to explore subsurface properties. In this paper, we report on the application of a new stochastic inversion method called Greedy Annealing Importance Sampling (GAIS) (Xue et al., 2011), which is a combination of global optimization methods and stochastic inference methods. This new method is designed for an optimal balance between computational efficiency and accuracy of estimation. In additional to the new inversion algorithm, we use geostatistics to draw initial models for inversion. We apply our inversion algorithm to a 3D seismic dataset from Eagle Ford. Unlike the conventional geostatistical simulation, our approach uses GAIS that is capable of estimating uncertainty and makes use of transversely isotropic media for synthetic seismogram calculation. The results show that this new method resolves the formation interfaces and the large impedance contrast between Eagle Ford and Buda. Also, GAIS provides better lateral continuity of and lateral variation in inverted impedances. In addition, the quality of inverted S-impedance is improved significantly, because the anisotropy is accounted for in our approach.