In order to study the characteristics of road traffic flow, a car-following model based on vehicle-mounted high-precision GPS car-following test data was studied. Combining the deep learning theory and data-driven method, a long and short term memory (LSTM) car-following model based on particle swarm optimization (PSO) was constructed. Firstly, the vehicle track data was cleaned and smoothed, and the parameters related to driving behavior, such as acceleration, headway, and the relationship between speed and car-following distance were examined. Car-following status screening rules were formulated based on this analysis. Secondly, a PSO-LSTM model considering time series was constructed to identify the sample set of car-following data. The current time's preceding car speed, headway, and the preceding car's headway at the previous time were utilized as inputs for the model to predict the car-following speed at the current time. Subsequently, the performance of the PSO-LSTM model was verified using high-precision GPS data from 25 car-following tests. Finally, traditional machine learning support vector regression (SVR) model and deep learning LSTM model were selected for comparison in order to validate the superiority of the proposed model. The results demonstrate that the LSTM model based on PSO achieves a prediction accuracy as high as 0.993, outperforming the SVR and LSTM models overall. Moreover, the prediction error index mean absolute percentage error (MAPE) is reduced by 60.02% and 1.52% compared to SVR and LSTM, respectively. The PSO-LSTM model, optimized through the PSO algorithm for hyperparameter tuning, provides a better simulation of the car-following behavior of vehicles.