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 real world, 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 prediction of any classifier faithfully by learning an interpretable model locally around the predicted instance. As an extension of LIME, this paper proposes an high-interpretability and high-fidelity local explanation method, known as Local Explanation using feature Dependency Sampling and Nonlinear Approximation (LEDSNA). Given an instance being explained, LEDSNA enhances interpretability by feature sampling with intrinsic dependency. Besides, LEDSNA improves the local explanation fidelity by approximating nonlinear boundary of local decision. We evaluate our method with classification tasks in both image domain and text domain. Experiments show that LEDSNA's explanation of the back-box model achieves much better performance than original LIME in terms of interpretability and fidelity.