High-quality superconducting thin films play an important role in the application and basic research of high-Tc superconductivity. In these aspects, iron-based superconductors feature the merits of rich physical phenomena and high superconducting critical parameters (including the transition temperature Tc, the upper critical field Hc2 and the critical current density Jc). The recently discovered high-Tc (Li,Fe)OHFeSe superconductor proves to be an important material for the studies of the mechanism and application of unconventional high-Tc superconductivity. However, due to the hydroxyl ion inherent in the compound, none of the conventional high-temperature synthesis methods is applicable for (Li,Fe)OHFeSe materials in bulk and thin film forms. Recently, by developing a hydrothermal ion-exchange technique, we have synthesized for the first time big and high-quality single crystals of (Li,Fe)OHFeSe (2015 Phys. Rev. B 92 064515). Here in this paper, we brief our most recent progress on growing a high-quality single-crystalline superconducting film of (Li,Fe)OHFeSe (2017 Chin. Phys. Lett. 34 077404). The film has been prepared on a LaAlO3 substrate by a hydrothermal epitaxial method. The high crystalline quality of the film is verified by X-ray diffraction (XRD). The XRD measurements show a single (001) orientation with a small crystal mosaic of 0.22 in terms of the full width at half maximum of the rocking curve, as well as an excellent in-plane orientation revealed by the -scan of (101) plane. Its bulk superconducting transition temperature Tc of 42.4 K is determined by both zero electrical resistance and diamagnetism measurements. Based on systematic magnetoresistance measurements, the upper critical field Hc2 is estimated to be 79.5 T and 443 T for the magnetic field perpendicular and parallel to the ab plane, respectively. Moreover, a large critical current density Jc of a value over 0.5 MA/cm2 is achieved at ~20 K. Such a (Li,Fe)OHFeSe film therefore is not only important for the fundamental research for understanding the high-Tc mechanism, but also promising for the applications in high-performance electronic devices and large scientific facilities such as superconducting accelerator.