Abstract: Targets localization is an issue of theoretical importance and practical significance in radar signal processing. In order to solve the problems of the traditional targets localization algorithm of Frequency Diverse Array (FDA) radar, such as large amount of calculation and the true location of the target deviates from the spatial discretized sampling grid. In this paper, an off-grid targets localization algorithm by a double-pulse Frequency Diverse Array (FDA) radar based on Sparse Bayesian Learning (SBL) is put forward by combining FDA radar characteristics with off-grid Sparse Bayesian model. The FDA radar transmits two pulses with zero and non-zero frequency offsets, respectively, and then estimates the azimuth angle and slant range of targets based on the off-grid sparse Bayesian model. This approach can be interpreted as detecting the targets in angle dimension when the FDA radar emits pulse with zero offset and then localizing them in range dimension by properly choosing the non-zero frequency offset. According to the simulation, the algorithm can maintain high estimation accuracy even under a coarse sampling grid, have shown advantages over conventional ones, which proves the effectiveness and reliability of the method.