The formation pore pressure is an important basic parameter in the process of oil and gas drilling from well design to well completion. It is an important basis for the rational design of drilling plans and analysis of wellbore stability, and accurate calculation of formation pore pressure is an important prerequisite for ensuring drilling safety and improving drilling efficiency. In order to overcome the problems of insufficient accuracy and low calculation efficiency of traditional formation pore pressure calculation methods, this paper takes into account that both the drilling process and the formation deposition process have a certain degree of sequentiality and complex nonlinearity, so this article proposes a method to calculate formation pore pressure by combining a Long Short-Term Memory (LSTM) neural network and an error Back Propagation (BP) neural network based on drilling-logging-recording data. The LSTM layer in the neural network is used to extract the serial feature information in the multi-source data of drilling, logging, and recording, and the BP layer in the neural network is used to construct a nonlinear mapping relationship between characteristic information and formation pore pressure. The field data of an oilfield was cleaned and processed, and 18 parameters such as drilling time, weight on bit, dc-exponent, sonic time difference, and density logging were optimized through comprehensive correlation analysis and drilling experience knowledge, and the LSTM-BP formation pore pressure calculation model was carried out with training, validation and testing, and using the grid search method to analyze and optimize the 5 hyperparameters of the LSTM-BP model, including the number of LSTM layers, the number of neural units in the LSTM unit gate, the number of BP layers, the number of neurons in the BP layer, and the activation function. The mean absolute error of the best single well calculation model and the best adjacent well calculation model were 4.92 MPa and 2.34 MPa, the root mean square error were 6.65 MPa and 3.03 MPa, and the mean relative error were 4.36% and 8.31%. Finally, the LSTM-BP model is compared with the optimized traditional BP neural network model, LSTM neural network model, and Support Vector Machine (SVM) model. The results show that the accuracy of the LSTM-BP neural network model established in this paper is higher than that of the BP neural network model, LSTM neural network model, and SVM model, which show that the LSTM-BP formation pore pressure calculation model proposed in this paper has a high calculation accuracy.