Conventional physics-based or experimental-based approaches for gas turbine combustion tuning are time consuming and cost intensive. Recent advances in data analytics provide an alternative method. In this paper, we present a cross-disciplinary study on the combustion tuning of an F-class gas turbine that combines machine learning with physics understanding. An artificial-neural-network-based (ANN) model is developed to predict the combustion performance (outputs), including NOx emissions, combustion dynamics, combustor vibrational acceleration, and turbine exhaust temperature. The inputs of the ANN model are identified by analyzing the key operating variables that impact the combustion performance, such as the pilot and the premixed fuel flow, and the inlet guide vane angle. The ANN model is trained by field data from an F-class gas turbine power plant. The trained model is able to describe the combustion performance at an acceptable accuracy in a wide range of operating conditions. In combination with the genetic algorithm, the model is applied to optimize the combustion performance of the gas turbine. Results demonstrate that the data-driven method offers a promising alternative for combustion tuning at a low cost and fast turn-around.