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In this paper a new expression of the signal-to-interference-noise ratio (SINR) for single cell multicarrier code division multiple access (MC-CDMA) wireless system in a frequency-selective Rayleigh fading channel is derived and investigated. The expression is much simplified compared to previous research. The SINR performance in uplink channels with frequency-selective Rayleigh fading is shown by computer simulation. It is assumed that the proposed system suffers single path fading. Numerical results indicate that the system performs better than that of the conventional DS-CDMA system. The result of the analysis will provide relevant information to design the physical layer protocol for 4G mobile communications system.