We demonstrated a long-range and centimeter-spatial-resolution optical frequency domain reflectometry (OFDR) system based on an ultra-linear broadband optical frequency sweep. The high nonlinear sweeping effect of the distributed feedback (DFB) diode laser was suppressed by a pre-distortion method, ensuring that the injection-locking process remained stable during fast tuning over a large span. An optical linear frequency sweep (LFS) with a sweep range and sweep rate of up to 60 GHz and 15 THz/s, respectively, was ultimately obtained by optimizing the injection-locking system. The high performance OFDR based on the proposed LFS achieved a sampling spatial resolution of 1.71 mm. Furthermore, distributed strain sensing was implemented with high-spatial resolutions of about 5 cm and 7 cm in the measurement range over 1 km and 2 km, respectively.