The petroleum industry operates under great uncertainty. Achieving an efficient approach to quantify uncertainty in oil production models is of key importance in supporting decision-makers to find suitable strategies for mitigating risks and maximizing profit. Uncertainty quantification is commonly performed based on the Monte Carlo approach and this is a very time-consuming process by using the physics-based models developed by reservoir simulators. To solve this challenge, data-driven proxy models which are less complex and computationally efficient can be used as an alternative. This paper aims to investigate the functionality of the ANN method in developing proxy models for uncertainty quantification of oil production from advanced wells. The investigation is conducted through a case study for uncertainty assessment of cumulative oil and water productions from a long horizontal well with ICD completion and zonal isolation in a synthetic reservoir for 10 years. In this study, the Eclipse® reservoir simulator is used for developing the base case model and it is coupled with MATLAB® for generating the required data sets to train and test the ANN proxy model. According to the obtained results, the trained and developed ANN proxy model can predict the production of oil and water from advanced wells accurately with a mean error of less than 4%. Besides, the proxy model is 150 times faster than the Eclipse model and can solve the challenge of the time-consuming process of uncertainty quantification.