For circuit design, various compact models for graphene field-effect transistors (GFETs) have been developed. However, the consistency between them is poor, since study on the mechanism of operation of GFETs is still immature and the models were derived based on different understandings. Herein, we propose another approach for circuit-level description of GFETs based on a prior knowledge input neural network modeling method. By virtue of the neural network's learning ability, it can accurately describe different GFETs without an exact description of their mechanism of operation. Basic knowledge on GFETs and an adaptive genetic algorithm are employed to improve the precision of the neural network, resulting in performance significantly exceeding that of a traditional, multilayer perceptron network. The universality of the method is verified by detailed tests using two different datasets. Its applicability for circuit design is demonstrated by relevant circuit simulations in a Verilog-A implementation.