Despite its long history, synthesizing n-type polycrystalline Ge layers with high-electron mobility on insulating substrates has been difficult. Based on our recently developed solid-phase crystallization technology, here, we have demonstrated the highest recorded electron mobility (450 cm2 V−1 s−1) for Ge-based polycrystalline thin films on insulating substrates. The underlayer type and small amount of Sn addition were the key parameters controlling both the density and barrier height of the grain boundaries in the P-doped polycrystalline Ge layers. The low growth temperature (≤400 °C) allowed us to develop a GeSn layer on a heat-resistant polyimide film, which exhibited the highest electron mobility (200 cm2 V−1 s−1), as a semiconductor thin film synthesized directly on a flexible substrate. These achievements herald the development of high-performance polycrystalline Ge-based devices on inexpensive glass and flexible plastic substrates.