Electron-beam propagation from a gas-filled diode is investigated. The beginning portion of the electron beam pulse creates an ion channel not only inside the diode but also in the region beyond the anode. A theoretical model is developed for the space-charge-limited current of a relativistic electron beam propagating through an ion channel. A simple analytical expression for the space-charge-limited current is obtained within the context of a thin-beam approximation, where the conducting-tube radius is much larger than the beam radius. The beam current propagating through an ion channel is measured experimentally for a mildly relativistic electron beam. Whenever the ion density inside the diode is the same as the beam electron density, the diode is short-circuited. The ion-channel density at the short-circuiting time is calculated numerically and is used to estimate the space-charge-limited current. It is shown that the experimental data agree well with the analytical results predicted by the theoretical model.