Despite outperforming humans in different supervised learning tasks, complex machine learning models are criticised for their opacity which make them hard to trust especially when used in critical domains (e.g., healthcare, self-driving car). Understanding the reasons behind the decision of a machine learning model provides insights into the model and transforms the model from a non-interpretable model (black-box) to an interpretable one that can be understood by humans. In addition, such insights are important for identifying any bias or unfairness in the decision made by the model and ensure that the model works as expected. In this paper, we present ILIME, a novel technique that explains the prediction of any supervised learning-based prediction model by relying on an interpretation mechanism that is based on the most influencing instances for the prediction of the instance to be explained. We demonstrate the effectiveness of our approach by explaining different models on different datasets. Our experiments show that ILIME outperforms a state-of-the-art baseline technique, LIME, in terms of the quality of the explanation and the accuracy in mimicking the behaviour of the black-box model. In addition, we present a global attribution technique that aggregates the local explanations generated from ILIME into few global explanations that can mimic the behaviour of the black-box model globally in a simple way.