We demonstrate a high-resolution frequency-modulated continuous-wave dual-frequency LIDAR system based on a monolithic integrated two-section (TS) distributed feedback (DFB) laser. In order to achieve phase locking of the two lasers in the TS-DFB laser, the sideband optical injection locking technique is employed. A high-quality linear frequency-modulated signal is achieved from the TS-DFB laser. Utilizing the proposed LIDAR system, the distance and velocity of a target can be measured accurately. The maximum relative errors of distance and velocity measurement are 1.6% and 3.18%, respectively.