We have seen complex deep learning models out-performing human benchmarks in many areas (e.g. computer vision, natural language processing). Clever architectures and higher model complexity are two of the major drivers of such outstanding performances. Higher model complexity generally makes the decision-making process of a model opaque to human perception. But understanding the decision-making process is very important for many reasons including enhancing trust in the model’s prediction, improving model robustness, gaining actionable insight from why a model made a particular prediction and discovering new knowledge about a problem. Model explainability has been an active area of research for some time now, but the problem is still far from being solved. An established way of model explanation is to assign a score to each variable (also known as variable attribution), which represents the importance of the variable in a particular prediction of a model. In a lot of techniques, the scoring process involves distributing the output to each variable. This is challenging when the model is complex and consists of a high degree of interaction terms. A coalition game theoretic approach called Shapley Value provides a fair way to tackle the challenge. However, the growth of computation time of the exact Shapley Values is exponential in the number of variables. Hence, many attribution techniques use approximations instead of the exact Shapley Value as attribution. In this manuscript, we propose a novel variable attribution technique called Appley (short for Approximate Shapley) by approximating the Shapley Values in linear time. Moreover, we show that the “Appley” attributions are generally closer to the exact Shapley Values than an existing well-known and comparable attribution technique.