In allusion to the coupling relationship among radial velocity variation, range migration, and Doppler spread of a maneuvering target, a Dynamic Programing (DP)-based Weighted Adaptive Coherent Integration (DPWACI) detection method is proposed. The target energy could be efficiently integrated along its trajectory by the proposed method. The main idea of DPWACI is the joint execution of the three operations: the weighted DP procedure that could accurately search the current position and velocity of the target; the improved coherent integration that could calibrate the Doppler shift during the entire process with a large phase spread; and the adaptive step that could make the integration time suitable for each velocity searching bin. The proposed method is applicable to a target with an arbitrary motion without estimating its specific movement parameters. Simulation results and performance comparisons show the exactitude and superiority of the proposed method.