A landslide is a type of natural disaster that has the highest frequency, the widest distribution and the heaviest losses worldwide; landslides seriously threaten human life and property and major engineering facilities. Therefore, it is important to improve landslide displacement prediction technology to avoid and mitigate landslide disasters. A landslide displacement prediction method based on a chaotic Gaussian mutation sparrow search algorithm-optimised BP neural network (CG-SSA-BP) is proposed to address the problems of the traditional sparrow search algorithm (SSA)-optimised BP (SSA-BP) neural network; it tends to fall into local optima, and it has slow convergence and a low prediction accuracy for landslide displacement prediction. This paper takes the Baishui River landslide in the Three Gorges reservoir area as the research object, and the double exponential smoothing (DES) method is used to decompose the landslide displacement into a trend term and a periodic term to solve the nonlinear landslide system problem. The results show that the prediction model based on CG-SSA-BP has a better prediction accuracy and better stability compared with the model based on SSA-BP.