The continuous collision between Tian Shan and Tarim Basin causes not only the uplift of mountains, but also the earthquakes across the entire Tian Shan, particularly in the transient zone from mountains to the adjacent basins, where the critical infrastructures and residents are seriously under threat from these earthquake hazards. On 19^th January, 2020, an earthquake occurred in the Kalpintage fold thrust belt in the southwest Tian Shan foreland. We call this event the 2020 M_W6.0 Kalpintage earthquake, which is the first moderate earthquake captured by modern geodetic measurement techniques. This event therefore provides a rare opportunity to look into the local tectonics and seismic risk in southwest Tian Shan. In this study, we obtained the coseismic deformation of 2020 M_W6.0 Kalpintage earthquake from Sentinel-1A SAR and strong motion data, and then inverted its kinematic slip model. We derived the InSAR interferograms from both ascending and descending tracks. Both of them present similar deformation patterns, two deformation peaks over the Kalpintage anticline. That means: 1)The surface deformation is dominated by vertical displacement, and 2)the coseismic rupture plane is highly suspected to be the shallowly dipping decollement at the base of the sediment cover. We got the 3-D displacements of 6 strong motion stations by double integrating the strong motion acceleration signals. The result shows tiny displacement on the strong motion stations, except for the Xikeer station, which locates at the front of the Kalpintage anticline, where the InSAR interferograms are seriously incoherent. Two slip models can equally fit to the ascending and descending InSAR interferograms: One is a strike slip model with strike of N-S, the other is a thrust model with strike of E-W. This ambiguity in the slip models for the M_W6.0 Kalpintage earthquake is caused by 1)the extremely small dip angles of the causative fault, 2)the inherent shortcomings of the InSAR measurements i.e. the 1-D measurements along the line of sight, the polar orbiting direction of the SAR satellite, and 3)the serious atmospheric delay due to contrasting topography in southwest Tian Shan. We did not distinguish the two ambiguous models with InSAR data due to the weak constraints of InSAR for this event. However, the two quite different slip models show the same spatial dimension and position beneath the Kalpintage anticline, also the same seismic slip vector moving toward the Tarim Basin. We then presumed the two slip models refer to the same fault plane, the weak decollement at the base of the sediment cover, and its rupture released the compressive strain in this fold and thrust belt in the southwest Tian Shan front. The confusing problem is neither the strike slip model nor the thrust model can explain the displacement derived from strong motion. The simple error estimates show small uncertainty in the strong-motion-derived displacement, but we cannot really know the real errors without the comparison to the collocated continuous GNSS observation. Because of the discrepancy between the strong motion displacement and InSAR-derived slip model, we speculate the inelastic deformation occurred in front of the Kalpintage anticline where thick weak sediments exist. We think this earthquake ruptured the decollements in the lower sediments bounded by the adjacent anticlines, which are uplifted in this event. The M_W6.0 Kalpintage earthquake balanced the stress accommodated during the convergence of the Tian Shan and Tarim Basin. We managed to explain all of the ruptures in the southwest Tian Shan by combining the regional tectonic, geophysical data and the available earthquake catalogues with good quality and then estimated the earthquake hazards. The earthquakes, including 1902 M_W7.7 karshigar, 1996 M_W6.3 Jiashi, 1997—2003 Jiashi sequence and 2020 M_W6.0 Kalpintage earthquake, can be explained in one frame, the underthrusting of the Tarim Basin toward the southwest Tian Shan. Our calculation suggests that a M_W7.0+ event could be generated around Kalpintage anticline belt if without barriers on the decollements.