Abstract: ‍ ‍Frequency-agile radars are known for their low probability of interception and strong anti-interference capabilities. However， the rapid frequency hopping between pulses leads to non-uniform phase variations in the signal， which renders conventional detection methods of moving targets inapplicable. To address the estimation of range-velocity parameters for targets in frequency-agile radars as well as issues such as false target detection and true target amplitude loss， this study established a sparse signal processing model based on range-Doppler， transforming the parameter estimation problem into a sparse reconstruction issue. This study proposes a sparse adaptive and iterative weighted reconstruction （SAIWR） algorithm. Initially， the algorithm selects atoms based on their correlation with the dictionary matrix and performs a secondary screening through regularization conditions. Then， in each iteration， the extended step size is adaptively matched to the sparsity of the signal， continuing the search for the optimal set of atoms. Finally， the weight matrix is adjusted during the iteration according to the correlation between the atoms and dictionary matrix， enhancing the role of target atoms in the signal reconstruction process. This achieves radar target scene reconstruction and false target suppression when the number of targets is unknown. When adaptively inverting diagonal loading matrices， the algorithm utilizes the matrix inversion lemma， reducing the computational load. Computer simulation experiments demonstrate that the proposed algorithm accurately estimates the target parameters of frequency-agile radars in scenarios with adjacent and small targets. Compared with the existing regularized adaptive matching pursuit （RAMP） and sparse Bayesian learning （SBL） algorithms， the SAIWR algorithm offers higher reconstruction accuracy and a lower false alarm rate.