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Frisch-ring CdZnTe detectors have demonstrated both good energy resolution, <1% FWHM at 662 keV, and good efficiency in detecting gamma rays, highlighting the strong potential of CdZnTe materials for such applications. We are designing a hand-held gamma-ray spectrometer based on Frisch-ring detectors at Brookhaven National Laboratory. It employs an 8 times 8 CdZnTe detector array to achieve a high volume of 19.2 cm3, so greatly improving detection efficiency. By using the front-end application-specific integrated circuits (ASICs) developed at BNL, this spectrometer has a small profile and high energy-resolution. It includes a signal processing circuit, digitization and storage circuits, a high-voltage module, and a universal serial bus (USB) interface. In this paper, we detail the system's structure and report the results of our tests with it.