In order to utilise the position and attitude information of a Celestial Navigation System (CNS) to aid a Strapdown Inertial Navigation System (SINS) and make it possible to achieve long-range and high-precision navigation, a new SINS/CNS integrated navigation scheme based on overall optimal correction is proposed. Firstly, the optimal installation angle of the star sensor is acquired according to the geometric relationship between the refraction stars area and the star sensor's visual field. Secondly, an analytical method to determine position and horizontal reference is introduced. Thirdly, the mathematical model of the SINS/CNS integrated navigation system is established. Finally, some simulations are carried out to compare the navigation performance of the proposed SINS/CNS integrated scheme with that of the traditional gyro-drift-corrected integration scheme. Simulation results indicate that in the proposed scheme, without the aid of SINS, CNS can provide attitude and position information and the errors of the SINS are able to be estimated and corrected efficiently. Therefore, the navigation performance of the proposed SINS/CNS scheme is superior to that of a more traditional scheme in long-range flight.