[Purposes] This paper aims to improve the accuracy of construction cost prediction, and provide an important basis for the early investment decision of the project. [Methods] For the characteristics of high-dimensional nonlinear relationships between small sample data and the characteristic indexes of project cost in engineering practice, a cost prediction model (SSA-LSSVM) based on the sparrow search algorithm (SSA) optimized least squares support vector machine (LSSVM) is constructed. Firstly, the input index data of residential project cost is processed by principal component analysis to reduce data redundancy. Secondly, the SSA is used to optimize the regularization parameter c and the kernel function parameter σ in the LSSVM model to help determine the parameters of the LSSVM model. Finally, the processed data is imported into the constructed model for training and prediction, and the model prediction performance is evaluated by three metrics, that is correlation coefficient, mean absolute percentage error and root-mean-square error. [Findings] SSA-LSSVM model has better generalization ability and prediction accuracy compared with LSSVM model, LSSVM model optimized by grey wolf algorithm and back propagation neural network. [Conclusions] The model built in this study can accurately and efficiently predict the actual residential project cost, which can provide some reference for the pre-project investment decision.