This paper describes the data acquisition system used for data readout from the PMT channels of a segmented detector of reactor antineutrinos with active shielding. Theoretical approach to the data acquisition is described and two possible solutions using QDCs and digitizers are discussed. Also described are the results of the DAQ performance during routine data taking operation of DANSS. DANSS (Detector of the reactor AntiNeutrino based on Solid Scintillator) is a project aiming to measure a spectrum of reactor antineutrinos using inverse beta decay (IBD) in a plastic scintillator. The detector is located close to an industrial nuclear reactor core and is covered by passive and active shielding. It is expected to have about 15000 IBD interactions per day. Light from the detector is sensed by PMT and SiPM.