One of significant challenges in the metallic additive manufacturing (AM) is the presence of many sources of uncertainty that leads to variability in microstructure and properties of AM parts. Consequently, it is extremely challenging to repeat the manufacturing of a high-quality product in mass production. A trial-and-error approach usually needs to be employed to attain a product with high quality. To achieve a comprehensive uncertainty quantification (UQ) study of AM processes, we present a physics-informed data-driven modeling framework, in which multi-level data-driven surrogate models are constructed based on extensive computational data obtained by multi-scale multi-physical AM models. It starts with computationally inexpensive metamodels, followed by experimental calibration of as-built metamodels and then efficient UQ analysis of AM process. For illustration purpose, this study specifically uses the thermal level of AM process as an example, by choosing the temperature field and melt pool as quantity of interest. We have clearly showed the surrogate modeling in the presence of high-dimensional response (e.g. temperature field) during AM process, and illustrated the parameter calibration and model correction of an as-built surrogate model for reliable uncertainty quantification. The experimental calibration especially takes advantage of the high-quality AM benchmark data from National Institute of Standards and Technology (NIST). This study demonstrates the potential of the proposed data-driven UQ framework for efficiently investigating uncertainty propagation from process parameters to material microstructures, and then to macro-level mechanical properties through a combination of advanced AM multi-physics simulations, data-driven surrogate modeling and experimental calibration.