Orthogonal frequency division multiplexing (OFDM), which uses a number of narrowband orthogonal sub-carriers, is a promising transmission technique. Also multi-carrier code division multi-access (MC-CDMA), which combines OFDM and frequency-domain spreading, has been attracting much attention as a future broadband wireless access. It was shown that MC-CDMA has lower channel capacity than OFDM, due to inter-code interference (ICI) resulting from orthogonality distortion caused by frequency-selective fading. Recently, many ICI cancellers have been proposed to mitigate the effect of ICI. In this paper, we derive a channel capacity expression for MC-CDMA assuming perfect ICI cancellation taking into account both frequency diversity gain and space diversity gain and compare it to that of OFDM. Furthermore, we derive a channel capacity expression for the case of imperfect ICI cancellation to discuss the impact of the residual ICI.