A novel blood pressure estimation method based on long short-term memory neural network, one of the recurrent neural networks being commonly used nowadays, is proposed in this paper for better chronic diseases monitoring. Along with the neural network, a newly proposed ambulatory blood pressure (ABP) processing technique called Two-stage Zero-order Holding (TZH) algorithm has also been presented in the paper. The proposed methodology has the advantages over traditional blood pressure estimation algorithms which are based on Pulse Transit time (PTT). The paper addresses the effectiveness of the algorithm by computing the Root-Mean-Squared Errors (RMSE) between the BP estimated and the ground truth. Our algorithm shows precise systolic blood pressure and diastolic blood pressure estimation with the average RMSE values in 2.751 mmHg and 1.604 mmHg respectively across the sample used. Experimental results suggest that BP estimation based on LSTM has great potential to be embedded into monitoring system for better accuracy and generalization.