In this paper, a precoder design algorithm using spatial signal synthesis with selected multiple antenna subsets for hybrid multiple-input multiple-out-put (MIMO) systems is proposed. The hybrid MIMO systems are expected to be implemented in high frequency bands. To reduce power consumption and increase the bandwidth of a transmit signal, the resolution of phase shifters and the number of quantization levels in digital-analog (D/A) converters have to be limited. A baseband precoder needs to take the effect of quantization into account. On the other hand, when the number of transmit antennas is larger than that of receive antennas, spatial signal synthesis can be realized. The selection of antenna sets also needs to take the effect of quantization into account. In this paper, a transmit antenna selection scheme that improves the spectral efficiency by spatial signal synthesis with multiple antenna subsets is proposed. Numerical results obtained through computer simulation show that the proposed scheme with two antenna subsets of four transmit antennas and two receive antennas improves the spectrum efficiency by about 1.0 bit/s/Hz when the number of transmit and receive are 4.