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Gamma Ray Array Detector (GRAD) is one of External Target Facility (ETF) subsystems at the Heavy Ion Research Facility at Lanzhou. The trigger subsystem of the GRAD has been developed based on Field Programmable Gate Array (FPGAs) and PXI interface. The GRAD trigger subsystem makes prompt L1 trigger decisions to select valid events. These decisions are made by processing the hit signals from 1024 CsI scintillators of the GRAD. According to the physical requirements, the GRAD trigger subsystem generates 12-bit trigger signals that are passed to the ETF global trigger system. In addition, the GRAD trigger subsystem generates trigger data that are packed and transmitted to the host computer via PXI bus for off-line analysis. The trigger processing is implemented in the front-end electronics and one FPGA of the trigger module. The logic of PXI transmission and reconfiguration is implemented in the other FPGA of the trigger module. The reliable and efficient performance in the Gamma-ray experiments demonstrates that the GRAD trigger subsystem is capable to satisfy the physical requirements., Comment: This paper has been accepted by