In mobile 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 with the limited bandwidth. Eigenbeam space division multiplexing (E-SDM) is known as one of MIMO multiplexing techniques. In this paper, we propose frequency-domain SC E-SDM for SC transmission. In frequency-domain SC 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 inter-symbol interference (ISI). In this paper, the transmit power allocation and adaptive modulation based on the equivalent channel gains after performing FDE are applied. The BER performance of the frequency-domain SC E-SDM in a severe frequency-selective Rayleigh fading channel is evaluated by computer simulation.