In the next generation mobile communication systems, multiple-input multiple-output (MIMO) multiplexing is an indispensable technique to achieve very high-speed data transmission with a limited bandwidth. In MIMO multiplexing, it is necessary to estimate the channels between transmit and receive antennas for signal detection. In this paper, we propose a minimum mean square error (MMSE) channel estimation using cyclic delay pilot for single-carrier (SC)-MIMO multiplexing. In the proposed channel estimation, the same pilot block is altered through the addition of different cyclic delays and transmitted from different antennas at the same time for simultaneous estimation of all channels between transmit and receive antennas. We evaluate by computer simulation the bit error rate (BER) performance of MIMO multiplexing using the proposed channel estimation and compare it to those using time-multiplexed pilot based channel estimation (TMP-CE) and code-multiplexed pilot based channel estimation (CMP-CE).