In this letter, we focus on the problem of direct position determination (DPD) for moving targets. Compared with the traditional two-step localization methods, the DPD methods is more robust at low signal-to-noise ratio (SNR). However, to guarantee the optimal location results the computational complexity of DPD with grid search is too high, especially for moving targets. Therefore, we propose a new DPD method for moving targets with low computational complexity. First, using a proposed cost function, we obtain the position information from the received array signals directly. Second, we use the method of successional difference which averages the difference result of position over time to extract the velocity. It avoids the multi-dimensional parameters grid search and reduces the the computational complexity greatly. Simulation results demonstrate that the proposed algorithm outperforms other methods in a wide range of scenarios, especially at low SNR.