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 stability and operation flexibility 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 introduce the GEneral Memristive transistor (GEM) model to address this challenge. The GEM model incorporates time-dependent differential equation, a voltage-controlled moving window function, and a nonlinear current output function, enabling precise representation of both switching and output characteristics in memristive transistors. Compared to previous models, the GEM model demonstrates a 300% improvement in modeling the switching behavior, while effectively capturing 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.