This paper addresses the problems of inaccurate positioning and heading dispersion in complex environments of the GNSS/INS tightly integrated navigation system running on the vehicle. Based on the implicit constraints that the vehicle's velocity is zero and its attitude and gyroscope outputs remain unchanged, an augmented zero-velocity constraint-assisted GNSS/INS tightly integrated navigation algorithm is proposed. First, the algorithm performs zero-velocity detection, based on horizontal velocity and gyroscope modulus. And then zero linear velocity, zero angular velocity and unchanged pitch angle and roll angle at the front and rear moments when vehicle's velocity is zero are used as observation constraints for the integrated navigation. Vehicle-mounted test has shown that the proposed GNSS/INS tightly integrated navigation aided by augmented zero-velocity constraint greatly improves stability compared to conventional integrated navigation algorithm. Specifically, the position accuracy of the integrated navigation is improved by 24.56%, the velocity accuracy by 81.69%, the attitude accuracy by 80.43%, and the overall positioning performance of the vehicle is enhanced by 62.23%.