Since X-ray pulsar navigation system (XNAV) has better anti-interference and autonomy, a novel X-ray pulsar integrated navigation method combining celestial navigation system (CNS) and strapdown inertial navigation system (SINS) is proposed in this paper. Using XNAV and CNS to simultaneously correct the output of SINS not only solves the problem of error accumulation in SINS, but also ensures that the system has a high degree of autonomy and anti-interference. In order to further improve navigation accuracy, a suboptimal multiple fading extended Kalman filter (SMFEKF) is used for information fusion between XNAV and the other two navigation methods. Finally, numerical simulations show that the integrated navigation algorithm not only has higher accuracy than SINS and CNS/SINS, but also can output attitude information that XNAV cannot output. And navigation accuracy increases with the number of pulsars. Besides, the accuracy of XNAV/CNS/SINS using SMFEKF is significantly better than EKF.