Inverse synthetic aperture radar (ISAR) imaging for the sparse aperture data is affected by considerable artifacts, because under-sampling of data produces high-level grating and side lobes. Noting the ISAR image generally exhibits strong sparsity, it is often obtained by sparse signal recovery (SSR) in case of sparse aperture. The image obtained by SSR, however, is often dominated by strong isolated scatterers, resulting in difficulty to recognize the structure of target. This paper proposes a novel approach to enhance the ISAR image obtained from the sparse aperture data. Although the scatterers of target are isolated in the ISAR image, they should be associated with the neighborhood to reflect some intrinsic structural information of the target. A convolutional reweighted l1 minimization model, therefore, is proposed to model the structural sparsity of ISAR image. Specifically, the ISAR image is reconstructed by solving a sequence of reweighted l1 problems, where the weight of each pixel used for the next iteration is calculated from the convolution of its neighbor values in the current solution. The problem is solved by the alternating direction of multipliers (ADMM) and linearized approximation, respectively, to improve the computational efficiency. Experimental results based on both simulated and measured data validate that the proposed algorithm is effective to enhance the ISAR image, robust to noise, and more impressively, very efficient to implement.