We reported a graphene field-effect transistor (GFET) based on CVD Ge-based graphene and primarily investigated the low-temperature electrical characteristics. The self-alignment technique was used to fabricate GFET to reduce parasitic effects and improve transconductance and cut-off frequency. To further explore the electrical properties, we studied the direct current and radio frequency characteristics of the GFET over a temperature range from 4.2 K to 300 K, considering the temperature-dependent resistivity of intrinsic Ge. The DC characteristic of the GFET for 110 nm gate length, particularly the transconductance performance, exhibits a tiny variation of only ~ 5% across this temperature range. However, the cut-off frequency experiences a considerable increase, improving several tens of times when the temperature decreases to 4.2 K, with a maximum value of 3.49 GHz. This work illustrates a meaningful advancement in applying GFETs in the lowtemperature, high-frequency domain.