Arterial blood pressure (ABP) serves as a pivotal clinical metric in cardiovascular health assessments, with the precise forecasting of continuous blood pressure assuming a critical role in both preventing and treating cardiovascular diseases. This study proposes a novel continuous non-invasive blood pressure prediction model, DSRUnet, based on deep sparse residual U-net combined with improved SE skip connections, which aim to enhance the accuracy of using photoplethysmography (PPG) signals for continuous blood pressure prediction. The model first introduces a sparse residual connection approach for path contraction and expansion, facilitating richer information fusion and feature expansion to better capture subtle variations in the original PPG signals, thereby enhancing the network’s representational capacity and predictive performance and mitigating potential degradation in the network performance. Furthermore, an enhanced SE-GRU module was embedded in the skip connections to model and weight global information using an attention mechanism, capturing the temporal features of the PPG pulse signals through GRU layers to improve the quality of the transferred feature information and reduce redundant feature learning. Finally, a deep supervision mechanism was incorporated into the decoder module to guide the lower-level network to learn effective feature representations, alleviating the problem of gradient vanishing and facilitating effective training of the network. The proposed DSRUnet model was trained and tested on the publicly available UCI-BP dataset, with the average absolute errors for predicting systolic blood pressure (SBP), diastolic blood pressure (DBP), and mean blood pressure (MBP) being 3.36 ± 6.61 mmHg, 2.35 ± 4.54 mmHg, and 2.21 ± 4.36 mmHg, respectively, meeting the standards set by the Association for the Advancement of Medical Instrumentation (AAMI), and achieving Grade A according to the British Hypertension Society (BHS) Standard for SBP and DBP predictions. Through ablation experiments and comparisons with other state-of-the-art methods, the effectiveness of DSRUnet in blood pressure prediction tasks, particularly for SBP, which generally yields poor prediction results, was significantly higher. The experimental results demonstrate that the DSRUnet model can accurately utilize PPG signals for real-time continuous blood pressure prediction and obtain high-quality and high-precision blood pressure prediction waveforms. Due to its non-invasiveness, continuity, and clinical relevance, the model may have significant implications for clinical applications in hospitals and research on wearable devices in daily life.