<p>Kalman filter based on maximum correntropy criterion (MCC) has robust characteristics against non-Gaussian heavy-tailed impulsive noises. To apply this filter to nonlinear systems, MCC-based cubature Kalman filter (MCC-CKF) is designed and applied to tightly coupled inertial navigation system (INS)/ultra-wideband (UWB) integrated navigation. CKF provides a solution with minimum mean square error (MMSE) characteristics to the estimation problem of a system with process noise and measurement noise satisfying Gaussian distributions. However, since UWB measurements may include various types of non-Gaussian errors in addition to noise, it is difficult to optimally integrate INS and UWB information using the existing CKF. In order to add robust properties against these errors, CKF is redesigned based on MCC. In particular, MCC-CKF is designed for a system in which both the system and measurement functions are nonlinear, and this filter does not require a measurement matrix that is essential for the existing MCC-based Kalman filter. As a result of analyzing the performance of the MCC-CKF-based INS/UWB integrated navigation through simulation, it was confirmed that the impact on the UWB errors is minimized by tuning only the <i>R</i> matrix value corresponding to the UWB channel including non-Gaussian error. Furthermore, the performance of the proposed filter is reconfirmed through field testing.</p>