Hypertension is a major risk factor for CardioVascular Disease （CVD）， and continuous blood pressure monitoring is crucial for CVD prevention. To address the limitations of the existing models in multi-scale feature representation， long-term dependency modeling， and inter-task information interaction， a data-driven blood pressure prediction model named Multi-scale Transformer with Enhanced Graph neural network （MTEG） was proposed to integrate a multi-scale convolution， an enhanced Transformer encoder， a channel attention mechanism， and a graph attention-based multi-task learning strategy to model local and global features of PhotoPlethysmoGraphy （PPG） signals jointly. Specifically， a multi-scale feature extraction module was designed to capture local patterns across different temporal scales in PPG signals， while a Transformer encoder with Rotary Position Embedding （RoPE） and relative position bias was employed to model long-term dependencies in blood pressure variations， a feature-aware enhancement module was introduced to strengthen the response of channels related to blood pressure changes， and a multi-task feature aggregation module was constructed to achieve information collaboration among the prediction tasks of Systolic Blood Pressure （SBP）， Diastolic Blood Pressure （DBP）， and Mean Arterial Pressure （MAP）. Experimental results show that MTEG achieves the Mean Absolute Error （MAE） of 4.92， 2.68， and 2.59 mmHg in SBP， DBP， and MAP predictions， respectively. Predictions for DBP and MAP comply with the standards of the Association for the Advancement of Medical Instrumentation （AAMI） and achieve grade A of the British Hypertension Society （BHS） standard， while SBP prediction achieves grade B of the BHS standard， verifying the reliability and clinical application potential of the proposed model.