This paper proposes a sequentially iterative equalizer based on Kalman filtering and smoothing (SIEKFS) for multiple-input multiple-output (MIMO) systems under frequency selective fading channels. In the proposed SIEKFS, an iteration consists of sequentially executed subiterations, and each subiteration performs equalization and detection procedures of the symbols transmitted from a specific transmit antenna. During this subiteration, all available observations for the transmission block are utilized in the equalization procedures. Furthermore, the entire soft estimate of the desired symbols to be detected does not participate in the equalization procedures of the desired symbols, i.e., the proposed SIEKFS performs input-by-input equalization procedures for a priori information nulling. Therefore, compared with the original iterative equalizer based on Kalman filtering and smoothing, which performs symbol-by-symbol equalization procedures, the proposed SIEKFS can also perform iterative equalization based on the Kalman framework and turbo principle, with a significant reduction in computation complexity. Simulation results verify that the proposed SIEKFS achieves suboptimum error performance as the size of the antenna configuration and the number of iterations increase.