Through the study of microseismic focal mechanisms, information such as fracture orientation, event magnitude, and in situ stress status can be quantitatively obtained, thus providing a reliable basis for unconventional oil and gas exploration. Most source inversion methods assume that the medium is isotropic. However, hydraulic fracturing is usually conducted in sedimentary rocks, which often exhibit strong anisotropy. Neglecting this anisotropy may cause errors in focal mechanism inversion results. We have developed a microseismic focal mechanism inversion method that considers velocity anisotropy in a vertically transverse isotropic medium. To generate synthetic data, we adopt the moment-tensor model to represent microearthquake sources. We use a staggered-grid finite-difference method to calculate synthetic seismograms in anisotropic media. We perform seismic moment-tensor (SMT) inversion with only P-waves by matching the synthetic and observed waveforms. The synthetic and field data sets are used to test the inversion method. For the field data set, we investigate the inversion stability using randomly selected partial data sets in the calculation. We pay special attention to analyze the sensitivity of the inversion. We test and evaluate the impact of noise in the data and errors in the model parameters (, , and ) on the SMT inversion using synthetic data sets. The results indicate that, for a surface acquisition system, our method can tolerate moderate noise in the data and deviations in the anisotropy parameters can cause errors in the SMT inversion, especially for dip-slip events and the inverted percentages of non-double-couple (DC) components. According to our study, including anisotropy in the model is important to obtain reliable non-DC components of moment tensors for hydraulic fracturing-induced microearthquakes.