Most of fiber-optic pressure sensors used in shock wave measurements are based on deformations of sensing elements. These approaches result in low dynamic pressure ranges for these sensors used in the air. A novel fiber-optic method based on the relationship between pressure and the acceleration of a diaphragm is proposed to obtain peak reflected pressure of shock waves in the air. The optical sensor is designed with a thin circular diaphragm as the sensing element, and the Fabry-Perot optical interferometry is used to detect the acceleration of the diaphragm. Shock tube and explosive-blast experiments prove that the proposed fiber optic method is feasible and has the advantages of no calibration, high precision and fast response time. The proposed fiber-optic pressure method has potential in practical applications for shock wave measurements.