The gravity gradient is the second derivative of gravity potential. A gravity gradiometer can measure the small change of gravity at two points, which contains more abundant navigation and positioning information than gravity. In order to solve the problem of passive autonomous, long-voyage, and high-precision navigation and positioning of submarines, an aided navigation method based on strapdown gravity gradiometer is proposed. The unscented Kalman filter framework is used to realize the fusion of inertial navigation and gravity gradient information. The performance of aided navigation is analyzed and evaluated from six aspects: long voyage, measurement update period, measurement noise, database noise, initial error, and inertial navigation system device level. When the parameters are set according to the benchmark parameters and after about 10 h of simulation, the results show that the attitude error, velocity error, and position error of the gravity gradiometer aided navigation system are less than 1 arcmin, 0.1 m/s, and 33 m, respectively.