Micro-electromechanical systems and inertial measurement units (MEMS-IMUs) show great advantages in terms of price and size. Nevertheless, due to limitations of technology, their observations are easily affected by the surrounding environment (temperature, vibration, and electronic noise). Most methods resist the effect of gross errors by adjusting covariance matrices in the integrated navigation of a global navigation satellite system (GNSS) and inertial navigation system (INS). We propose a motion model-assisted integrated navigation method on the basis of a constant yaw rate and velocity (CTRV) model, which serves as a constraint condition and detects gross errors by a Chi-squared test. The results of the CTRV are used to correct the carrier state from INS mechanization. A field test was carried out to verify the performance of the CTRV-assisted method. Compared with a robust Kalman filter, the method improves the horizontal accuracy of position and velocity by more than 87% and 68%, respectively, in a medium-precision loosely and tightly coupled system, and of the velocity and attitude by more than 52% and 20%, respectively, in a low-precision loosely and tightly coupled system. Therefore, the CTRV-assisted method can significantly enhance the performance of GNSS/MEMS-IMU integrated navigation systems.