This work presents a novel approach to estimate aircraft performance parameters, specifically fuel flow consumption, by using Deep Learning (DL) on Quick Access Record (QAR) data collected by a narrow-body aircraft. The uniqueness of this approach is that it is purely driven by data, and not by a physics model. Our models can estimate fuel flow consumption for specific flight conditions during different flight phases. The results show that, compared to more standard models used by manufacturers (e.g., Base of Aircraft Data (BADA)), we reduced the error in the estimation of fuel consumption significantly just by using DL. Respect to the baseline BADA nominal, the error is reduced from a Mean Absolute Error (MAE) of 258.67 kg/hour down to 55.89 kg/h, 54.25 kg/h, and 49.83 kg/h, using BADA calibrated, Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM)/Convolutional Neural Network (CNN) respectively. Also, the Mean Absolute Percentage Error (MAPE) went from 10.55% (BADA nominal) down to 2.29%, 2.23% and 2.04%, for BADA calibrated, MLP and LSTM/CNN respectively. These models have multiple applications such as fuel analytics, flight planning, health monitoring and post-flight efficiency assessment, with a tangible potential impact on the aviation industry.