In order to meet the needs of long-term, high-precision and low-cost navigation of underwater vehicles, a strapdown gravity passive navigation system is composed of a single-axis rotating strapdown inertial navigation system(SINS) based on laser gyro, a log, a depth gauge, a strapdown gravimeter based on fiber optic gyroscope and a digital gravity anomalies. The position of the carrier is given by a single-axis rotating SINS based on laser gyro; An underwater strapdown gravity measurement system is formed of a strapdown gravimeter based on fiber optic gyroscope, log and depth gauge, the position information provided by the axis-rotating strapdown inertial navigation system, the speed information provided by the log and the water depth information provided by the depth gauge are used as observations, the extended Kalman filter is applied to estimate the specific force of accelerometer in the local-level frame, the low-pass filtering is used to obtain the gravity value and the gravity anomaly value in real time; according to the digital gravity anomaly map stored in the computer, the relative extreme value method is used to calculate the position of the carrier. At the end of 2019, the strapdown gravity passive navigation system carried out a long-term shipboard experiment, and the experiment data of the system was processed offline. The experiment results show that: the carrier position error is less than 1 grid size of gravity anomaly map in the matching sea region.