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Silicon Photomultiplier (SiPM) has been demonstrated to be a high performance PET sensor as alternative to conventional photomutiplier tubes. The aim of this work is to develop a PET detector module with compact SiPM device which consists of 3×3 SiPM arrays (4×4 pixels each array,3.17×3.17 mm2 each pixel). A compact design of readout electronics is proposed based on discretized position-sensitive readout circuits (DPC) and time based readout ASIC. The function of the ASIC is to convert all signals' energy and timing information into digital timing pulses which can be processed by back-end simple Time-Digital-Convertor (TDC). So we get highly integrated electronics because the traditional Analog-Digital-Convertor (ADC) and Constant-Fraction-Discriminator (CFD) are replaced. A temperature-dependent gain control module including a microcontroller, a DAC and a DC-DC converter is designed to stabilize the gain of SiPM arrays against the variance of ambient temperature, which is based on the temperature sensor and serial identification chip intergrated in the SiPM array package. An preliminary experimental study was conducted, in which one SiPM array was coupled to a 6×6 LYSO crystal block. With a resistor charge-division chain readout circuit, a flood histogram map was acquired in which the crystals were clearly identifiable. With the correction of the gain control module,the maximum gain drift of SiPM decreases from 79.67% to 11.03% as the temperature varies from 27°C to 50°C. The result indicates that the developed gain control module can contribute to improving the stability of SiPM based PET detector. Through some basic tests, the ASIC has demonstrated good performances of linearity and uniformity. We conclude that the proposed design is feasible for developing a compact SiPM PET detector module.