Neuromorphic devices, with their distinct advantages in energy efficiency and parallel processing, are pivotal in advancing artificial intelligence applications. Among these devices, memristive transistors have attracted significant attention due to their superior symmetry, stability, and retention characteristics compared to two-terminal memristors. However, the lack of a robust model that accurately captures their complex electrical behavior has hindered further exploration of their potential. In this work, we present the GEneral Memristive transistor model (GEM), a comprehensive voltage-controlled model that addresses this gap. The GEM model incorporates a state-dependent update function, a voltage-controlled moving window function, and a nonlinear current output function, enabling precise representation of the electrical characteristics of memristive transistors. In experiments, the GEM model not only demonstrates a 300% improvement in modeling the memory behavior but also accurately captures the inherent nonlinearities and physical limits of these devices. This advancement significantly enhances the realistic simulation of memristive transistors, thereby facilitating further exploration and application development.