Compressive Sensing (CS) is an emerging technique in Internet of Medical Things (IoMT) application especially for smart wearable devices to prolong the sensor lifetime, and enable a continuous healthcare monitoring system. This paper describes the performance of CS on our wrist-based cuff-less biosensor for estimating blood pressure (BP) continuously. The proposed biosensor offers a novel BP estimation method by only using the biosignal from subject wrist. A CS technique is implemented to encrypt and reduce the data transmission load of the dual biosignal, which include impedance plethysmography (IPG) and photo plethysmography (PPG). Therefore, multiple compression ratio (CR) were tested to the original signal. We further compare the CS-based extracted features called pulse transit times (PTTs). Based on our experiments, CS-based PTT value that calculated from the IPG peak point to the PPG max2 point (F2), achieved the best correlation coefficient (R) of -0.85 and -0.43 to the systolic BP and diastolic BP, respectively. These results suggest that the implementation of CS on our proposed wrist biosensor is suitable for non-intrusive, yet long-term continuous BP monitoring.