Silicon thin films with sub-1 mu m thickness are of technological significance in many electronic and energy conversion devices. While a number of previous works have investigated the in-plane thermal conductivity of silicon films, less reported is their cross-plane thermal conductivity, particularly at sub-1 mu m thickness. Here, we report on the cross-plane thermal conductivity of sub-1 mu m, undoped, polycrystalline silicon films (75 and 246 nm) with columnar grain structure at room temperature. Using an optical pump-probe thermoreflectance metrology and a semi-classical phonon transport model, we find the cross-plane thermal conductivity to be 4.5 +/- 0.8 and 12.5 +/- 2.3 W m(-1) K-1 for the 75 and 246 nm films, respectively. To the best of our knowledge, the cross-plane thermal conductivities we report here are the lowest ever reported for undoped polycrystalline silicon films with columnar grain structure, which can be ascribed to the impact of increased phonon scattering by a higher density of defects as compared to previous data. Given that a significant reduction in phonon thermal conductivity is required to enhance the thermoelectric energy conversion efficiency, our findings may be promising particularly for thermoelectric energy conversion applications.