Cuff-less blood pressure (BP) is a potential method for BP monitoring because it is undisturbed and continuous monitoring. Existing cuff-less estimation methods are easily influenced by signal noise and non-ideal signal morphology. In this study we propose a novel well-designed Convolutional Neural Network (CNN) model named Deep-BP for BP estimation task. The structure of Deep-BP can help to capture more underlying data features associated with BP than handcrafted features, thus improving the robustness and estimation accuracy. We carry out experiments with and without calibration procedure in training stage to evaluate the performance of new method in different application scenarios. The experiment results show that the Deep-BP model achieves high accuracy and outperforms existing methods, in the experiments both with and without calibration.