A new space-time (ST) code design is proposed based on the design criteria of space-time codes, which is applied to the MIMO systems with fewer receive antennas than transmit antennas. The space-time codes, referred to as full diversity lossless capacity (FDLLC) ST code, achieve full transmit diversity and loss-less equivalent channel capacity for ST precoded systems. Combined FDLLC-ST codes with channel codes, ST bit interleaved coded modulation (ST-BICM) system is constructed and an iterative detector/decoder is em-ployed at the receiver. Simulations are presented. It is proved that the proposed design has good performance compared with other ST precoded MIMO systems.