In wireless communications, the channel consists of many resolvable paths with different time delays, resulting in a severely frequency-selective fading channel. The frequency-domain equalization (FDE) can take advantage of the channel selectivity and improve the bit error rate (BER) performance of the single-carrier (SC) transmission. Recently, multi-input multi-output (MIMO) multiplexing is gaining much attention for achieving very high speed data transmissions under limited bandwidth. Eigenbeam space division multiplexing (E-SDM) is known as one of MIMO multiplexing techniques. In this paper, we propose frequency-domain E-SDM for SC transmission. In frequency-domain E-SDM, the orthogonal transmission channels to transmit different data in parallel are constructed at each orthogonal frequency. At a receiver, FDE is used to suppress the ISI. In this paper, for high spectrum efficiency, the transmit power allocation and the adaptive modulation based on the equivalent channel gains after performing FDE are applied. The transmission performance of the frequency-domain E-SDM in a severe frequency-selective Rayleigh fading channel is evaluated by computer simulation.