An organic field‐effect transistor based on a squaraine fiber is studied, where the electric conductance values of the bulk and accumulation channel are comparable. The measured current–voltage characteristics are decomposed into two components, one representing the bulk and the other the accumulation channel. For small gate voltage (Vg), the output characteristics of the channel are described as a superposition of the Ohmic, space‐charge‐limited current, and trap‐filled‐limited (TFL) conduction mechanisms. The traps near the source are filled with electrons injected from source via the source‐gate electric field, but the traps near the drain could be filled only with the source‐drain electric field (Vd). The higher the gate voltage, the larger is the density of electrons injected from the source into the accumulation channel, the larger the density of free electrons, the larger the density of the trapped electrons, and the larger the drain voltage up to which the modified Child's law exists. θ is the fraction of the free electrons. For large voltage Vg, all traps are filled with the source‐gate electric field, and, as a result, only Ohm's and Child's laws () are observed. The electron mobility in the accumulation channel features a linear dependence on the gate voltage.