It has been shown in the literature that, the inverse synthetic aperture radar (ISAR) echo can be seen as sparse and the ISAR imaging can be implemented by sparse recovery approaches. In this paper, we propose a new parametric weighted L1 minimization algorithm for ISAR imaging based on the parametric sparse representation of ISAR signals. Since the basis matrix used for sparse representation of ISAR signals is determined by the unknown rotation parameter of a moving target, we have to estimate both the ISAR image and basis matrix jointly. The proposed algorithm can adaptively refine the basis matrix to achieve the best sparse representation for the ISAR signals. Finally the high-resolution ISAR image is obtained by solving a weighted L1 minimization problem. Both numerical and real experiments are implemented to show the effectiveness of the proposed algorithm.