This paper proposes a novel method of error mitigation for stereo visual odometry (VO) applied in land vehicles. A non-holonomic constraint (NHC), which imposes physical constraint to the rightward velocity of a land vehicle, is implemented as an observation in an extended Kalman filter (EKF) to reduce the drift of stereo VO. The EKF state vector includes position errors in an Earth-centred, Earth-fixed (ECEF) frame, velocity errors in the camera frame, angular rate errors and attitude errors. All the related equations are described and presented in detail. In this approach, no additional sensors are used but NHC, namely velocity constraint in the right direction , is applied as an external measurement to improve the accuracy. Tests are conducted with the Karlsruhe Institute of Technology and Toyota Technological Institute (KITTI) datasets. Results show that the relative horizontal positioning error improved from 0⋅63% to 0⋅22% on average with the application of the velocity constraints. The maximum and root mean square of the horizontal error with velocity constraints are both reduced to less than half of the error with stand-alone stereo VO.