The current–voltage properties of CdZnTe radiation detectors are closely related to the device’s performance. In this paper, the mechanisms of the dark current transport in metal–semiconductor–metal structured CdZnTe radiation detectors are investigated by numerically simulating the static working states in a wide bias range. Simulated current–voltage characteristics are consistent with the experimental results. The major current components in various bias and barrier conditions are determined by comparing different current transport theories based on computed device working states. For Schottky contacts with large barrier heights, the reverse-biased cathode determines the current in the low bias range, where the current is limited by carrier generation and diffusion in the depletion layer. Otherwise, the current is restricted by the high-resistivity bulk material if the barrier is relatively small. However, when the device is fully depleted of electrons in the high bias range, injected holes from the forward-biased anode are the dominating mobile charges and produce a rapid current increase. For ohmic contacts where the electron barrier height is smaller than the hole barrier height, the current–voltage curves deviate from the linear relationship in the high bias range due to the electron space-charge-limited current. From the simulation results, a double-rectifying electrode configuration is proposed, which can significantly reduce the dark current of CdZnTe radiation detectors.