We present photometric redshifts for 1,031 X-ray sources in the X-ATLAS field using the machine-learning technique TPZ. X-ATLAS covers 7.1 deg2 observed with XMM-Newton within the Science Demonstration Phase (SDP) of the H-ATLAS field, making it one of the largest contiguous areas of the sky with both XMM-Newton and Herschel coverage. All of the sources have available SDSS photometry, while 810 additionally have mid-IR and/or near-IR photometry. A spectroscopic sample of 5,157 sources primarily in the XMM/XXL field, but also from several X-ray surveys and the SDSS DR13 redshift catalogue, was used to train the algorithm. Our analysis reveals that the algorithm performs best when the sources are split, based on their optical morphology, into point-like and extended sources. Optical photometry alone is not enough to estimate accurate photometric redshifts, but the results greatly improve when at least mid-IR photometry is added in the training process. In particular, our measurements show that the estimated photometric redshifts for the X-ray sources of the training sample have a normalized absolute median deviation, nmadh0.06, and a percentage of outliers, {eta}=10-14%, depending upon whether the sources are extended or point like. Our final catalogue contains photometric redshifts for 933 out of the 1,031 X-ray sources with a median redshift of 0.9.