Blood pressure (BP) monitoring is vital in daily healthcare, especially for cardiovascular diseases. However, BP values are mainly acquired through a contact-sensing method, which is inconvenient and unfriendly for BP monitoring. This paper proposes an efficient end-to-end network for estimating BP values from a facial video to achieve remote BP estimation in daily life. The network first derives a spatiotemporal map of a facial video. Then, it regresses the BP ranges with a designed blood pressure classifier and simultaneously calculates the specific value with a blood pressure calculator in each BP range based on the spatiotemporal map. In addition, an innovative oversampling training strategy was developed to handle the problem of unbalanced data distribution. Finally, we trained the proposed blood pressure estimation network on a private dataset, MPM-BP, and tested it on a popular public dataset, MMSE-HR. As a result, the proposed network achieved a mean absolute error (MAE) and root mean square error (RMSE) of 12.35 mmHg and 16.55 mmHg on systolic BP estimations, and those for diastolic BP were 9.54 mmHg and 12.22 mmHg, which were better than the values obtained in recent works. It can be concluded that the proposed method has excellent potential for camera-based BP monitoring in the indoor scenarios in the real world.