Full-spectrum solar energy utilization has drawn widespread attention for cascading solar energy utilization. The hybrid approach integrating photovoltaic generation and solar thermochemical reaction is attractive to convert full-spectrum solar energy into electricity and chemical energy. This paper proposes a concentrating solar photovoltaic/thermochemical hybrid system. Meanwhile, a spectral splitting concentrator is proposed and designed. The proposed concentrator consists of above-mirror and sub-mirror. The above-mirror enables the visible spectrum to be concentrated onto photovoltaics. The sub-mirror allows the infrared and ultraviolet spectra to be concentrated onto a solar thermochemical reactor. The design methodology based on ray tracing is described. The distribution of solar radiation on the photovoltaics and the thermochemical reactor is made analysis. The results show that solar radiation can be uniformly cast to the photovoltaic surface without using secondary optical element; the common solar flux concentration of thermochemical reactor is also mitigated. The proposed spectral splitting concentrator is introduced in the hybrid system. The total conversion efficiency of the solar energy can exceed 20%. Compared with individual photovoltaic electricity and solar thermal fuel, this hybrid system has the potential to increase the conversion efficiency of solar energy into both electricity and fuel, with greater than 5% absolute enhancement. The design of the spectral splitting concentrator provides the possibility of cascading utilization of full-spectrum solar energy.