In this letter, we introduce and investigate the RAKE combining receiver which is widely used in the code-division multiple access (CDMA) systems to the non-spectrum-spreading single-carrier transmission system. The initial estimate of the transmitted data is obtained by linear single-carrier equalizers, and then all the multipath signals are constructed from this initial solution and channel impulse response. By interference cancellation (IC) technique, we can acquire every multipath component in the received signal after cancelling the sum of all the other multipath signals constructed. Finally, all the components are combined together using selection combining (SC), equal gain combining (EGC) or maximal ratio combining (MRC), so that temporal diversity gain from the combined output can be obtained. Simulation results show that bit error rate (BER) performance of the new combining receiver based on zero forcing (ZF) and minimum mean square error (MMSE) equalizers can achieve the SNR gain dramatically in the SUI-5 wireless communication link.