The pulse arrival time (PAT), the difference between the R-peak time of electrocardiogram (ECG) signal and the systolic peak of photoplethysmography (PPG) signal, is an indicator that enables noninvasive and continuous blood pressure estimation. However, it is difficult to accurately measure PAT from ECG and PPG signals because they have inconsistent shapes owing to patient-specific physical characteristics, pathological conditions, and movements. Accordingly, complex preprocessing is required to estimate blood pressure based on PAT. In this paper, as an alternative solution, we propose a noninvasive continuous algorithm using the difference between ECG and PPG as a new feature that can include PAT information. The proposed algorithm is a deep CNN-LSTM-based multitasking machine learning model that outputs simultaneous prediction results of systolic (SBP) and diastolic blood pressures (DBP). We used a total of 48 patients on the PhysioNet website by splitting them into 38 patients for training and 10 patients for testing. The prediction accuracies of SBP and DBP were 0.0 ± 1.6 mmHg and 0.2 ± 1.3 mmHg, respectively. Even though the proposed model was assessed with only 10 patients, this result was satisfied with three guidelines, which are the BHS, AAMI, and IEEE standards for blood pressure measurement devices.