In marine vessel operations, fuel costs are major operating costs which affect the overall profitability of the maritime transport industry. The effective enhancement of using ship fuel will increase ship operation efficiency. Since ship fuel consumption depends on different factors, such as weather, cruising condition, cargo load, and engine condition, it is difficult to assess the fuel consumption pattern for various types of ships. Most traditional statistical methods do not consider these factors when predicting marine vessel fuel consumption. With technological development, different statistical models have been developed for estimating fuel consumption patterns based on ship data. Artificial Neural Networks (ANN) are some of the most effective artificial methods for modelling and validating marine vessel fuel consumption. The application of ANN in maritime transport improves the accuracy of the regression models developed for analysing interactive relationships between various factors. The present review sheds light on consolidating the works carried out in predicting ship fuel consumption using ANN, with an emphasis on topics such as ANN structure, application and prediction algorithms. Future research directions are also proposed and the present review can be a benchmark for mathematical modelling of ship fuel consumption using ANN.