In this paper, an iterative search algorithm to maximize system capacity in a time-varying MIMO distributed antenna system (DAS) is proposed. A common DAS model is employed, in which the transmit antennas are distributively located and the receiver can move arbitrarily in the region. Due to the small-scale fading effect and the receiver movement, the transmitters and receiver cannot obtain accurate channel state information (CSI) or optimize the system capacity. Therefore, we present a time-varying MIMO DAS model and corresponding channel evolution model to predict the time-varying channel. With the channel evolution model, the proposed iterative search algorithm can calculate the precoding matrix, and an iterative search process is employed to determine the optimal precoding matrix from a precoding matrix set. Meanwhile, error analysis show the error on the instantaneous mutual information with the proposed algorithm has a close relationship with the element number of the precoding matrix set and small-scale fading evolution coefficient. We also propose a non-uniform power allocation strategy which can improve the system capacity. Simulation results are presented to verity the analysis above and demonstrate the performance of system capacity with the proposed iterative search algorithm.