In order to design and evaluate the performance of low Earth orbit (LEO) satellite communication systems for the sixth generation (6G) mobile communications, an accurate channel model is essential. In this paper, a three-dimensional (3D) geometry-based stochastic model (GBSM) for 6G LEO satellite communication channels is established. The proposed channel model extends the quasi deterministic radio channel generator (QuaDRiGa) model and takes unique property of LEO satellite communication, such as Faraday rotation effect into account. The paper presents a single-bounce channel model, taking the spatial consistency of parameters into account and supporting simultaneous movements of the transmitter (Tx) and receiver (Rx). Finally, simulation experiments are conducted under different environments, center frequencies, and heights of satellites. Based on the proposed model, we analyze statistical properties of the channel including time autocorrelation function and delay spread (DS), which are in accordance with theoretical analysis and verify the correctness of the proposed model. Additionally, simulation results prove that parameters mentioned earlier have a considerable influence on channel characteristics and can help with guiding the design of communication systems.