Rich cardiovascular information is encompassed within the arterial blood pressure (ABP) waveform, offering valuable insights for the prevention and diagnosis of cardiovascular diseases. Despite the availability of several photoplethysmography (PPG)-based blood pressure prediction methods, they primarily focus on predicting systolic blood pressure (SBP) and diastolic blood pressure (DBP). This paper proposes a novel method for blood pressure measurement that predicts the entire ABP waveform from PPG signals. The proposed approach involves linearly mapping the PPG signal to a high-dimensional space and feature extraction using a Transformer encoder structure. A linear layer is then utilized to output the predicted ABP waveform, enabling the calculation of SBP and DBP. Experimental results demonstrate that the Transformer network provides an accurate fit to the actual ABP waveform in the MIMIC dataset, with predicted SBP and DBP errors averaging (3.76±5.66) mmHg and (2.20±3.77) mmHg, respectively. Additionally, the proposed method complies with the standards of the Association for the Advancement of Medical Instrumentation (AAMI) and achieves Grade A according to the British Hypertension Society (BHS) criteria.