The PoGOLite is a new balloon-borne instrument to measure the polarization of hard X-rays / soft gamma-rays in the 25-80 keV energy range for the first time. In order to detect the polarization, PoGOLite measures the azimuthal angle asymmetry of Compton scattering and the subsequent photo-absorption in an array of detectors. This array consists of 217 well-type phoswich detector cells (PDCs) surrounded by a side anti-coincidence shield (SAS) composed of 54 segments of BGO crystals. At balloon altitude, the intensity of backgrounds due to cosmic-ray charged particles, atmospheric gamma-rays and neutrons is extremely high, typically a few hundred Hz per unit. Hence the data acquisition (DAQ) system of PoGOLite is required to handle more than 270 signals simultaneously, and detect weak signals from astrophysical objects (100mCrab, 1.5cs-1 in 25-80 keV ) under such a severe environment. We have developed a new DAQ system consisting of front-end electronics, waveform digitizer, Field Programmable Gate Array (FPGA) and a microprocessor. In this system, all output signals of PDC / SAS are fed into individual charge-sensitive amplifier and then digitized to 12 bit accuracy at 24MSa/s by pipelined analog to digital converters. A DAQ board for the PDC records waveforms which will be examined in an off-line analysis to distinguish signals from the background events and measure the energy spectrum and polarization of targets. A board for the SAS records hit pattern to be used for background rejection. It also continuously records a pulse-height analysis (PHA) histogram to monitor incident background flux. These basic functions of the DAQ system were verified in a series of beam tests.