Cardiovascular disease (CVD) has become a common health problem of mankind, and the prevalence and mortality of CVD are rising on a year-to-year basis. Blood pressure (BP) is an important physiological parameter of the human body and also an important physiological indicator for the prevention and treatment of CVD. Existing intermittent measurement methods do not fully indicate the real BP status of the human body and cannot get rid of the restraining feeling of a cuff. Accordingly, this study proposed a deep learning network based on the ResNet34 framework for continuous prediction of BP using only the promising PPG signal. The high-quality PPG signals were first passed through a multi-scale feature extraction module after a series of pre-processing to expand the perceptive field and enhance the perception ability on features. Subsequently, useful feature information was then extracted by stacking multiple residual modules with channel attention to increase the accuracy of the model. Lastly, in the training stage, the Huber loss function was adopted to stabilize the iterative process and obtain the optimal solution of the model. On a subset of the MIMIC dataset, the errors of both SBP and DBP predicted by the model met the AAMI standards, while the accuracy of DBP reached Grade A of the BHS standard, and the accuracy of SBP almost reached Grade A of the BHS standard. The proposed method verifies the potential and feasibility of PPG signals combined with deep neural networks in the field of continuous BP monitoring. Furthermore, the method is easy to deploy in portable devices, and it is more consistent with the future trend of wearable blood-pressure-monitoring devices (e.g., smartphones and smartwatches).