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Graphene represents a high-performance material for field effect transistor (FET) manufacture. As a monolayer of carbon atoms, graphene offers flexibility, high carrier mobility, and transparency. Solution-gated graphene FETs based on flexible substrates have been developed for various applications. However, none of these FETs offer both flexibility and good insulation from the electrolyte simultaneously. This would restrict their applicability in certain areas, such as implantation. To solve this problem, we used commercially available graphene and polyimide to fabricate a graphene FET. Photosensitive polyimide was used as both substrate and insulator for our device. Two Au electrodes were used separately as source and drain, and the graphene was exposed to an electrolytic solution to form a solution-gated structure. In this paper, we have studied the resistance variation between source and drain during specific fabrication steps to optimize the fabrication process. By analyzing the FET performance after repeated bending tests, our device's performance reliability was also confirmed. When compared with similar published flexible devices, our FET showed higher transconductance and lower noise levels. Also, neural activities were recorded from cortex neurons cultured on graphene FET for the first time, which proved our device's biocompatibility and demonstrated its potential for electrophysiological applications. [ABSTRACT FROM AUTHOR]