In unconventional oil and gas development, the hydraulic fracturing (HF) technique is adopted to inject high-pressure fluid into the reservoir and change its pore-fracture connection structure to enhance production. HF causes the rocks to crack and generates microseismic events (with moment magnitudes of Mw≤3). Studying the microseismic focal mechanisms (shear/tensile/compressive HF cracks) is helpful for characterizing fracture geometry, monitoring the in situ stress state, and evaluating the HF effects to optimize the reservoir reconstruction for increasing production. Due to fluid injection activity, there may be non-double-couple (non-DC) mechanisms associated with HF cracks, and the commonly used double-couple (DC) source model may not be suitable. For the moment tensor (MT) source model, which is commonly used to describe the non-DC mechanism, inversion is challenging in single-well monitoring. The shear-tensile general dislocation (GD) model includes a non-DC mechanism, and its inversion is more constrained than the full MT model by specifying the focal mechanism as shear-tensile (or compressive) faulting. This paper reports a focal mechanism inversion case study of HF shear/tensile/compressive cracks in a tight oil reservoir in the Ordos Basin, China. We perform inversions based on the DC, GD, and MT source models, respectively. The results indicate that, for the downhole monitoring geometry in this study, most of the DC inversions fail to obtain proper synthetic and observed waveform fitting results, and the MT inversion results of different microseismic events exhibit worse consistencies than the GD results. According to the GD results, almost all the HF cracks can be explained as strike-slip faulting and most cracks correspond to non-negligible tensile/compressive mechanisms. Our study suggests that the GD source model is preferred in downhole microseismic monitoring to obtain reliable shear/tensile/compressive HF cracks, and the inverted non-zero slope angle reduces the uncertainty in fracturing geometry characterization, which will help improve microseismic studies and HF evaluations for enhanced resource recovery.