Observations of redshifted 21-cm radiation from neutral hydrogen during the epoch of reionization are considered to constitute the most promising tool to probe that epoch. One of the major goals of the first generation of low-frequency radio telescopes is to measure the 3D 21-cm power spectrum. However, the 21-cm signal could evolve substantially along the line-of-sight (LOS) direction of an observed 3D volume, since the received signal from different planes transverses to the LOS originated from different look-back times and could therefore be statistically different. Using numerical simulations we investigate this so-called light-cone effect on the spherically averaged 3D 21-cm power spectrum. For this version of the power spectrum, we find that the effect mostly ‘averages out’ and observe a smaller change in the power spectrum compared to the amount of evolution in the mean 21-cm signal and its rms variations along the LOS direction. Nevertheless, changes up to ∼50 per cent at large scales are possible. In general, the power is enhanced/suppressed at large/small scales when the effect is included. The cross-over mode below/above which the power is enhanced/suppressed moves towards larger scales as reionization proceeds. When considering the 3D power spectrum we find it to be anisotropic at the late stages of reionization and on large scales. The effect is dominated by the evolution of the ionized fraction of hydrogen during reionization and including peculiar velocities hardly changes these conclusions. We present simple analytical models which explain qualitatively all the features we see in the simulations.