Automatic target recognition (ATR) is one of the most demanding applications of synthetic aperture radar (SAR) in the field of radar reconnaissance and surveillance. Convolutional neural networks (CNNs) have been extensively employed for SAR-ATR and obtained remarkable accuracy. However, regarding the black-box nature and non-transparency in decision-making, CNN’s reliability is unsatisfactory. Recently, some progress has been made toward providing a visual explanation of CNN’s classification procedure. In this paper, we employ the Local Interpretable Model-agnostic Explanation (LIME) algorithm to propose an interpretability metric that can be helpful to evaluate the overall robustness of CNNs. Using the proposed framework, the user can infer what proportion of the results are based on target features, while the remainder is based on irrelevant correlations from the background clutter. The theoretical findings are validated by the public MSTAR database.