We propose a continuous, non-invasive blood pressure prediction method using the Conformer-LSTM model, which integrates a convolutional branch, Transformer branch, multi-scale cross-attention modules, adaptive spatial feature fusion, and a two-layer LSTM. This method predicts the ABP waveform from the PPG signal, from which systolic and diastolic blood pressures are derived. The model demonstrates minimal prediction error across a large dataset. Experimental results show a high correlation between the predicted ABP waveform from the MIMIC dataset and the actual waveform, with SBP and DBP prediction errors of (3.68±5.60) mmHg and (2.16±3.72) mmHg, respectively. The method complies with the American Association for the Advancement of Medical Devices (AAMI) standards and achieves an A-level rating according to the British Hypertension Society (BHS).