Quantum cascade laser (QCL) is a very attractive seed source for a multikilowatt pulsed CO2 lasers applied for driving extreme ultraviolet emitting plasmas. In this Letter, we investigate output beam properties of a QCL designed to address P18 and P20 lines of 10.6 micron band of CO2 molecule. In particular, output beam quality and stability are investigated for the first time. A well-defined linear polarization and a single-mode operation enabled a use of phase retrieval method for full description of QCL output beam. A direct, multi-image numerical phase retrieval technique was developed and successfully applied to the measured intensity patterns of a QCL beam. Very good agreement between the measured and reconstructed beam profiles was observed at distances ranging from QCL aperture to infinity, proving a good understanding of the beam propagation. The results also confirm a high spatial coherence and high stability of the beam parameters, the features expected from an excellent seed source.