A new all optical method for long term and continuous blood pressure measurement and monitoring without using cuffs is proposed by using Ballistocardiography (BCG) and Photoplethysmograph (PPG). Based on BCG signal and PPG signal, a time delay between these two signals is obtained to calculate both systolic blood pressure and diastolic blood pressure via linear regression analysis. The fabricated noninvasive blood pressure monitoring device consists of a fiber sensor mat to measure BCG signal and a SpO2 sensor to measure PPG signal. A commercial digital oscillometric blood pressure meter is used to obtain reference values and for calibration. It has been found that by comparing with the reference device, our prototype has typical means and standard deviations of 9+/-5.6 mmHg for systolic blood pressure, 1.8+/-1.3 mmHg for diastolic blood pressure and 0.6+/-0.9 bpm for pulse rate, respectively. If the fiber optic SpO2 probe is used, this new all fiber cuffless noninvasive blood pressure monitoring device will truly be a MRI safe blood pressure measurement and monitoring device.