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In this article, the Gaussian density of states (DOSs) in organic semiconductors is taken into account in order to derive a charge-based compact model for high-speed organic transistors. This physics-based analytical solution provides a continues current equation from below to above threshold regions with considering the deep and shallow trap densities in the organic material, power-law mobility model, and contact resistances effects. The proposed model is verified with the experimental data of our fabricated organic permeable base transistor (OPBT) and shows good agreement with the measurements. OPBTs are of great interest as vertical organic transistors and stand out due to their excellent performance, such as low-voltage operation and high transit frequency.