While deep learning makes significant achievements in Artificial Intelligence (AI), the lack of transparency has limited its broad application in various vertical domains. Explainability is not only a gateway between AI and society, but also a powerful feature to detect flaw of the models and bias of the data. Local Interpretable Model-agnostic Explanation (LIME) is a widely-accepted technique that explains the predictions of any classifier faithfully by learning an interpretable model locally around the predicted instance. However, the sampling operation in the standard implementation of LIME is defective. Perturbed samples are generated from a uniform distribution, ignoring the complicated correlation between features. Moreover, as the local decision boundary is non-linear for most complex networks, linear approximation may produce serious errors. This paper proposes an high-interpretability and high-fidelity local explanation method, known as Kernel-based LIME with Feature Dependency Sampling (KLFDS). Given an instance being explained, KLFDS enhances interpretability by feature sampling with intrinsic dependency. Besides, KLFDS improves the local explanation fidelity by approximating nonlinear boundary of local decision. We evaluate our method with image classification tasks and results show that KLFDS's explanation of the back-box model achieves much better performance than original LIME in terms of interpretability and fidelity.