Knowledge of the number, location, and interseismic slip rate of crustal faults is key to our understanding of the bulk mechanics of continental deformation. However, at present, the sparsity of geodetic velocity observations is a major limiting factor to improving our knowledge of the fault network. In this study, we combine long-swath interferometric synthetic aperture radar (InSAR) data to form an interseismic displacement rate map of over 1000 km length spanning the central Tibetan Plateau. Our dense geodetic observations indicate that strain varies smoothly in space without major concentration at previously mapped faults. Discrepancy between line-of-sight InSAR and GPS observations between 33°N–35°N could indicate ~4 mm/yr of surface uplift in this region. Derived strain rates are less than 5 × 10−8 yr−1 across the plateau. At the E-W left-lateral Kunlun fault, postseismic deformation following the 2001 Kokoxili earthquake results in an observed strain rate of 18 ± 4 × 10−8 yr−1 across a 100 km wide zone. Following removal of a viscoelastic model, we estimate an interseismic slip rate of 12 ± 2 mm/yr for the Kunlun fault. In the central Tibetan conjugate fault zone, the NE-SW striking Amdo-Sewa and NW-SE striking Beng Co faults have right-lateral slip rates of 6 ± 1 mm/yr and 1–4 ± 1 mm/yr, respectively. Meanwhile, the NE-SW striking Dongqiao fault has a left-lateral slip rate of 1–2 ± 1 mm/yr. The low slip rates we estimate for these faults indicate that tectonic strain is more broadly distributed across the plateau interior, perhaps due to the lithosphere being weak and without the abrupt strength contrasts that exist at the plateau margins.