Long-time coherent integration is known as a powerful method to detect the weak target. However, its effectiveness is limited by the target motion across range and Doppler bins. For the high-speed target, it is highly possible that the range bin crossing (RBC) problem occurs, and for maneuvering target, the Doppler bin crossing (DBC) problem cannot be neglected. In this paper, we propose a Radon dynamic path optimization and fixed point iteration method to deal with the RBC and DBC problem, and thus make the radar able to detect the high-speed maneuvering weak target effectively. Radon transform is essentially a parameter searching method to find the target range moving path. We derive a cost function based on the property of the slow time time-frequency and frequency-time matrix, and solve it with the dynamic path optimization and fixed point iteration algorithm. The proposed method does not demand any a priori information,and is free of the ambiguity of the velocity or the acceleration caused by the potential undersampling of the slow time. Both the simulated and real Radar echo signals validate the effectiveness of the proposed method.