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Charge transport of unintentionally doped GaSb nanowires was studied through the fabrication and analysis of nanowire field effect transistors (FETs). In this work, both temperature dependent and voltage dependent measurements demonstrate various operating regimes, including a transition from linear current-voltage behavior at low bias to a space-charge limited current (SCLC) at large bias. Analysis of the voltage and temperature variation in the SCLC regime provided quantitative information about the trap energy distribution in the nanowires, which, after thermal annealing, has been shown to reduce from 0.26 eV to 0.12 eV. The measurements also indicate that the GaSb nanowire FETs exhibit n-type behavior, which is likely due to oxygen impurities in the nanowires.