As one of the most prominent deformation features on Tibetan plateau, a series of N-S systematic rifts and V-shaped conjugate strike-slip faults are well developed in central-southern Tibet. However the mechanism for the formation of the rifts and conjugate strike-slip faults is still controversial. An east-west trending magnetotelluric (MT) array has been operated across the Gyaring Co Fault (GCF) at the northern end of the Xainza-Dingjye Rift (XDR) in Lhasa block. Three-dimensional (3-D) inversions are employed to image lithospheric resistivity structure. Combined with the previous north-south MT 3-D inversion result, electrical resistivity models reveal obvious conductive layer in the mid-to-lower crust beneath the XDR and apparent resistivity change in the vicinity of the GCF. The calculated depth-integrated conductivity shows that the weak mid-to-lower crust (~30 km- ~ 60 km) characterized by high conductance (≥ ~10,000 S) and melt fraction of ~5–13%, is mainly distributed between the Indus-Yarlung suture (IYS) and the GCF, whereas the relatively rigid crust characterized by low conductance (≤ ~2000 S) and melt fraction of ~2–4% appears to the northeast of the GCF. The weak mid-to-lower crust in southern Tibet and the abrupt difference in the resistivity characteristics of the mid-to-lower crust in the vicinity of the GCF, suggest the formation of the rifts in Lhasa block is closely associated with the weak mid-to-lower crust. Taken together with the upper mantle seismic features, the weak mid-to-lower crust is believed to be attributed to the underplated Indian plate. An alternative geodynamic model is presented to respond to the eastward extrusion during the ongoing N-S convergence between the Indian and Eurasian plates, that the rigid crust in central Tibet is sandwiched by the weak mid-to-lower crust in southern and northern Tibet, and the rifts form above the weak mid-to-lower crust, whereas the conjugate strike-slip faults develop on the rigid crust in central Tibet.