Hypertension is an important hazard to health. Blood pressure prediction is of great importance to avoid grave consequences caused by sudden increase of blood pressure. Based on traditional Long Short-Term Memory (LSTM) network, a multi-factor cue LSTM model for both short-term prediction (predicting blood pressure for the next day) and long-term prediction (predicting blood pressure for the next several days) was proposed to provide early warning of undesirable change of blood pressure. Multi-factor cues used in blood pressure prediction model included time series data cues (e.g. heart rate) and contextual information cues (e.g. age, BMI (Body Mass Index), gender, temperature).The change characteristics of time series data and data features of other associated attributes were extracted in the blood pressure prediction. Environment factor was firstly considered in blood pressure prediction and multi-task learning method was used to help the model to capture the relation between data and improve the generalization ability of the model. The experimental results show that compared with traditional LSTM model and the LSTM with Contextual Layer (LSTM-CL) model, the proposed model decreases prediction error and prediction bias by 2.5%, 3.8% and 1.9%, 3.2% respectively for diastolic blood pressure, and reduces prediction error and prediction bias by 0.2%, 0.1% and 0.6%, 0.3% respectively for systolic blood pressure.