Multicarrier code-division multiple-access (MC-CDMA) is one of the effective techniques to gain its multiple access capability, robustness against fading, and to mitigate the ISI. The conventional MC CDMA system is to transmit identical narrowband direct-sequence (DS) waveform in parallel over a number of subchannels uniformly. While in this paper, allowing for different quality-of-service (QoS) requirements for different users, we propose an improved multicarrier CDMA system with adaptive subcarrier allocation in which each user's waveform is transmitted over the use's favorite subchannel rather than over a number of subchannels. We analyzed the performance of our proposed system in frequency selective fading environment. Simulation results show that adaptive subcarrier allocation scheme, when used in conventional multicarrier CDMA system, the performance will be greatly improved