Along with the outstanding performance of the deep neural networks (DNNs), considerable research efforts have been devoted to finding ways to understand the decision of DNNs structures. In the computer vision domain, visualizing the attribution map is one of the most intuitive and understandable ways to achieve human-level interpretation. Among them, perturbation-based visualization can explain the "black box" property of the given network by optimizing perturbation masks that alter the network prediction of the target class the most. However, existing perturbation methods could make unexpected changes to network predictions after applying a perturbation mask to the input image, resulting in a loss of robustness and fidelity of the perturbation mechanisms. In this paper, we define class distortion as the unexpected changes of the network prediction during the perturbation process. To handle that, we propose a novel visual interpretation framework, Robust Perturbation, which shows robustness against the unexpected class distortion during the mask optimization. With a new cross-checking mask optimization strategy, our proposed framework perturbs the target prediction of the network while upholding the non-target predictions, providing more reliable and accurate visual explanations. We evaluate our framework on three different public datasets through extensive experiments. Furthermore, we propose a new metric for class distortion evaluation. In both quantitative and qualitative experiments, tackling the class distortion problem turns out to enhance the quality and fidelity of the visual explanation in comparison with the existing perturbation-based methods.