Computational microwave imaging (CMI) based on the frequency diversity metasurface apertures (FDMAs) is an emerging technology and has attracted wide attention. FDMA-based CMI (FDMA-CMI) can be considered as microwave compressive sensing imaging with the frequency diversity pattern of the FDMA being the sensing matrix and solved by sparse signal reconstruction algorithms. However, the imaging quality is affected by the sensing matrix error and off-grid error seriously. In this article, we propose a novel algorithm for FDMA-CMI, referred to as off-grid sparse Bayesian learning (SBL) method based on sinc interpolation (OGSISBL), by taking both the off-grid error and sensing matrix error into account. First, we establish the measurement model with both the off-grid error and sensing matrix error. Specifically, the off-grid error is represented as a set of parameters to be estimated in the measurement model, and the sensing matrix error is represented as the amplitude–phase drift of the transceiver channels of the imaging system due to the principle of the FDMA. Then, under the framework of the SBL, a robust imaging algorithm OGSISBL is developed via the variational Bayesian expectation maximization (VBEM), which can not only recover the amplitude and position of the return of the scattered, but also simultaneously calibrate the amplitude–phase drift of the transceiver channels and the off-grid error. The performance of the proposed algorithm is evaluated by both the simulation data and the measured data collected by the self-designed experimental FDMA-CMI system, and the results validate the effectiveness and robustness of the proposed method.