Graphene field-effect transistors (GFETs) are promising candidates for future nano-electronic circuitry with excellent radio frequency (RF) and microwave performance due to the ultra-high carrier mobility, large saturation velocity, and good electrical conductivity of the graphene channel. In this paper, a compact circuit-level model of GFETs is proposed for RF and microwave high-frequency applications. An improved double-gate monolayer short channel GFET with an agate length of 150 nm was first designed and fabricated by self-aligned gate processing, enabled by optimized organic, contamination-free graphene transfer, for realizing high working frequency up to 40 GHz. A compact, precise circuit-level model, including the linear and nonlinear operation of GFETs, is then proposed with model parameters extracted based on the test data from the fabricated GFETs. The proposed model is capable of precisely simulating the ambipolar status of GFETs working up to microwave frequency. The calculated errors of the S-parameters, the reflection coefficient, the gain, (all in decibel), and the I–V data (in decimal) are less than 3.5%, 4.1%, 3.1%, and 2.4%, respectively. By defining as the symbolically defined device module, the GFET model with gate dimensional scalability can be easily embedded in the common commercial simulators for RF and microwave circuit and system level designs.