The optical efficiency of a holographic spectrum-splitting optical system with transmission holographic lenses is investigated. Spectrum-splitting is a promising approach to improve the efficiency of photovoltaic (PV) systems. By removing the lattice-matching constraints, it is possible to utilize low-cost thin-film PV materials and fabrication techniques. Transmission holograms are fabricated with the recording of the interference patterns of two or more coherent beams. It is also possible to use converging construction wavefronts to record holographic gratings that are matched to the focusing beam from the primary concentrator optics. Experimental holograms are fabricated in dichromated gelatin, and high diffraction efficiency is obtained. A single holographic lens is used to divide a broad spectrum into two types of PV cells. The position and orientation of the PV cells are chosen to match the dispersion properties of the holographic lens. The optical transfer efficiency of the holographic lens is measured to be at the peak with fast transitions between the high diffraction efficiency and the high transmission spectral regions. With a GaAs solar cell and a 2.1-eV bandgap solar cell, the system efficiency is 31.0% under one-sun which is improved by 11.9% over the best single PV cell. The achievable system efficiency with the prototype filter is 96% compared to that of the ideal system.