The range resolution of inverse synthetic aperture radar (ISAR) imaging can be improved by directly increasing the bandwidth of the transmitted signal. However, it complicates the design of radar system hardware and increases the manufacturing cost. Aiming at solving the abovementioned problems, a multi-band ISAR fusion imaging method based on the multiple measurement vectors (MMV) model is proposed to improve the range resolution. First, a multi-band ISAR fusion imaging model based on the compressed sensing theory is established. Second, to improve the computational efficiency, a MMV accelerated improved linearized Bregman algorithm is proposed to solve the model. Nesterov’s acceleration gradient method and the condition number optimization of the sensing matrix are combined to further improve the iterative convergence speed. Finally, experimental results based on the simulation data and measured data verify the effectiveness and superiority of the proposed algorithm, which can achieve multi-band ISAR fusion imaging with higher imaging efficiency and better image quality.