Context. The XMM-Newton Distant Cluster Project is a serendipitous survey for clusters of galaxies at redshifts z ≥ 0.8 based on deep archival XMM-Newton observations. X-ray sources identified as extended are screened against existing optical all-sky surveys for galaxies, in case of candidate high-z clusters followed up with imaging at 4 m-class telescopes and, ultimately, multi-object spectroscopy at 8 m-class telescopes. Low-significance candidate high-z clusters are followed up with the seven-channel imager GROND (Gamma-Ray Burst Optical and Near-Infrared Detector) that is mounted at a 2 m-class telescope. Its unique capability of simultaneous imaging in the g , r , i , z , J, H, Ks bands enables the use of the photometric redshift technique. Aims. Observing strategy, data reduction and analysis, depth and accuracy of the simultaneous multi-wavelength photometry are discussed with the goal of establishing GROND as a useful instrument to confirm X-ray selected (high-z) clusters. Methods. The test case is XMMU J0338.7+0030, suggested to be at z ∼ 1.45 ± 0.15 (1σ) from the analysis of the z − H vs. H colour−magnitude diagram obtained from the follow-up imaging. Later VLT-FORS2 spectroscopy enabled us to identify four members, which set this cluster at z = 1.097 ± 0.002 (1σ). To reach a better knowledge of its galaxy population, we observed XMMU J0338.7+0030 with GROND for about 6 h. The publicly available photo-z code le Phare was used. Results. The Ks-band number counts of the non-stellar sources out of the 832 detected down to z ∼ 26 AB mag (1σ) in the 3.9×4.3 arcmin 2 region of XMMU J0338.7+0030 imaged at all GROND bands clearly exceed those computed in deep fields/survey areas at ∼20.5-22.5 AB mag. The photo-z's of the three imaged spectroscopic members yield z = 1.12 ± 0.09 (1σ). The spatial distribution and the properties of the GROND sources with a photo-z in the range 1.01-1.23 confirm the correspondence of the X-ray source with a galaxy over-density at a significance of at least 4.3σ. Candidate members that are spectro-photometrically classified as elliptical galaxies define a red locus in the i −z vs. z colour−magnitude diagram that is consistent with the red sequence of the cluster RDCS J0910+5422 at z = 1.106. XMMU J0338.7+0030 hosts also a population of bluer late-type spirals and irregulars. The starbursts among the photometric members populate both loci, consistently with previous results. Conclusions. The analysis of the available data set indicates that XMMU J0338.7+0030 is a low-mass cluster (M 200 ∼ 10 14 M ) at z = 1.1. With the photometric accuracy yielded by the present unoptimized multi-band observations with GROND, we not only confirm the spectroscopic redshift of this cluster but also show that it hosts a galaxy population that can still undergo significant bursts of star-formation activity.