Additive Manufacturing (AM) technology is being increasingly adopted in a wide variety of application areas because of its ability to rapidly produce, prototype, and customize designs. AM techniques has significant opportunities in nuclear materials with accelerated fabrication process and reduced cost. High-fidelity modeling and simulation of AM processes is being developed at the Idaho National Laboratory (INL) to support AM process optimization, and to fundamentally understand the various physical interactions involved. In this paper, we employ Bayesian inverse Uncertainty Quantification (UQ) to quantify the input parameter uncertainties in a MOOSE-based melt pool model for AM of nuclear fuels. Inverse UQ is the process to inversely quantify the input uncertainties while keeping model predictions consistent with measurement data. The inverse UQ process takes into account uncertainties from model, code and data while simultaneously characterizing the uncertain distributions in the input parameters, instead of only providing best-fit point estimates. We employ measurement data on melt pool geometry (lengths and depths) to quantify the uncertainties in several melt pool model parameters such as power absorption coefficient, material emissivity, etc. Simulation results using the posterior uncertainties have shown improved agreement with experimental data, compared to those using the prior nominal values. The resulting parameter uncertainties can be used to replace expert opinions in future uncertainty, sensitivity and validation studies.