This study aims to enable steady and speedy acquisition of Inverse Synthetic Aperture Radar (ISAR) images using sparse echo data. To this end, a Multiple Measurement Vectors (MMV) ISAR echo model is studied. This model is then combined with the Compressive Sensing (CS) theory to realize a class of MMV fast ISAR imaging algorithms based on the Linearized Bregman Iteration (LBI). The algorithms involve four methods, and the iterative framework, application conditions, and relationship between the four methods are given. The reconstructed performance of the methods, convergence, anti-noise, and selection of regularization parameters are then compared and analyzed comprehensively. Finally, the experimental results are compared with the traditional Single Measurement Vector (SMV) ISAR imaging algorithm; this comparison shows that the proposed algorithm delivers an improved imaging quality with a low Signal-to-Noise Ratio (SNR).