Mini-EUSO is a UV telescope which is developed by the JEM-EUSO collaboration to be placed on board the International Space Station (ISS) to carry out measurements of UV atmosphere airglow and transient luminous events (TLEs) in a wide field of view ($>$40$^\circ$) and high temporal resolution (2.5 $\mu$s). Mini-EUSO is developed to be a space qualified pathfinder of future JEM-EUSO missions. Optical system of the detector consists of two Fresnel lenses of 25 cm diameter. The focal surface is composed of 36 produced by Hamamatsu multi anode photomultiplier tubes (MAPMT), each with 64 pixels. The output signal of all 2304 pixels is digitized and then passed to the data processing system that was specially developed for the experiment and is being discussed in this work. Data processing system is based on produced by Xilinx ZYNQ chip that contains both programmable part (FPGA) and processor. Such combination in a single chip gives a big advantage for processing a data gathered from focal surface including fast multi-level trigger algorithms, data buffering, MAPMTs high voltage control algorithms, interfaces with front-end electronics and with the separate central processor unit for data storage. The multi-level trigger was developed for the mini-EUSO instrument to perform measurements in various time scales (temporal resolutions $2.5 \mu$s, 320 $\mu$s, 40 ms). This trigger was successfully implemented and tested.