The non-holonomic constraint (NHC) of vehicle motion can be used as the velocity observation information for the vehicle-integrated navigation system, which can effectively suppress the error accumulation of the inertial navigation system (INS). To fully exert the constraint function of NHC, it is significant to accurately estimate and compensate for the inertial measurement unit (IMU) stagger angle and NHC lever arm. This paper researched the NHC lever arm and estimated the IMU stagger angle and NHC lever arm simultaneously by three-dimensional dead reckoning and Kalman filter without an odometer. The results show that the proposed algorithm can accurately estimate the stagger angle and NHC lever arm of the high-precision INS and low-precision micro-electro-mechanical system (MEMS) INS, and the stagger angle error is less than 0.1°. The estimated NHC lever arm projection point is more in line with the NHC constraint condition than the IMU center, and it can significantly improve the auxiliary effect of NHC constraint and strengthen the performance of the vehicle-integrated navigation system.