In this paper, a new layered space-time coding scheme for flat fading MIMO channels is presented. Based on linear dispersive coding that preserves the channel capacity, the proposed scheme employs phase shifts among input symbols to maximize both diversity and coding gains without loss of mutual information. In addition, this coding scheme provides simple spatial multiplexing (channel layering) through antenna weighting. As a result, a class of linear block space-time codes can be designed to achieve various tradeoffs between performance and spectral efficiency. Simulation results are provided to show the merits of the proposed scheme compared to conventional schemes.